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Anguyennn

  • one year ago

Could someone please help me simplify 3-2(3x-4)(3x+4)-(x+2)(2x-1)?

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  1. anonymous
    • one year ago
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    Do you know the foil rule for expanding brackets?

  2. Anguyennn
    • one year ago
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    yes so I got 3-2(9x^2+12x-12x+16)-(2x^2-x+4x-2) is that correct?

  3. anonymous
    • one year ago
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    Yep thats right, now just times the number outside the brackets by everything inside.

  4. anonymous
    • one year ago
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    Simplify the inside of the brackets firstb to make it easier

  5. Anguyennn
    • one year ago
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    do you minus 3-2 first? .....so it would be 1(9x^2+12x-12x+16)-(2x^2-x+4x-2)?

  6. Anguyennn
    • one year ago
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    oh

  7. Anguyennn
    • one year ago
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    (9x^2+16)-(2x^2+3x-2)

  8. anonymous
    • one year ago
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    No you can't do that, the -2 is multiplies by brackets its a different type of term than the 3 by itslef, so you cant add them

  9. anonymous
    • one year ago
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    yeah what you did was right

  10. Anguyennn
    • one year ago
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    ok now do I multiply the first bracket with -2?

  11. anonymous
    • one year ago
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    but remeber only add things if they have the same thing, for example x^3 and x^2 cant add together, but x^2 and 2x^2 can add to 3x^3

  12. anonymous
    • one year ago
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    onceyou multiply the bracket by -2 you can start combining like terms (same power of x)

  13. Anguyennn
    • one year ago
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    but what about the 3?

  14. Anguyennn
    • one year ago
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    on the outside?

  15. anonymous
    • one year ago
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    leave that to last, you can only combine it with other numbers by itself (not multiplied by an x)

  16. Anguyennn
    • one year ago
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    so right now I am getting 3(-18x^2+32)-(2x^2-x+4x-2)

  17. anonymous
    • one year ago
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    just leave the 3, and you forgot about the x in the first bracket

  18. Anguyennn
    • one year ago
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    but it cancels out doesn't it? because 12x-12x is 0

  19. anonymous
    • one year ago
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    oh yeah true that i forgot :P

  20. Anguyennn
    • one year ago
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    haha its ok

  21. anonymous
    • one year ago
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    So you have 3-2(9x^2+12x-12x+16)-(2x^2-x+4x-2) this becomes 3 -2(9x^2 + 16) -(2x^2+3x-2) this becomes 3 -(18x^2-32) -2x^2-3x+2 this becomes 3 -18x^2 + 32 -2x^2 -3x +2

  22. anonymous
    • one year ago
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    Now combine like terms

  23. anonymous
    • one year ago
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    i make a mistake

  24. anonymous
    • one year ago
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    it should be -32

  25. anonymous
    • one year ago
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    on the last line (i screwed up a couple of lines up)

  26. Anguyennn
    • one year ago
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    no its positive

  27. Anguyennn
    • one year ago
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    its +32

  28. anonymous
    • one year ago
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    -2 x 16 = -32

  29. Anguyennn
    • one year ago
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    -2x-16=32

  30. anonymous
    • one year ago
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    of i see what was wrong

  31. Anguyennn
    • one year ago
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    because at the beginning its (3x-4)(3x+4)

  32. anonymous
    • one year ago
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    i accidentaly put +16 when it was -16

  33. Anguyennn
    • one year ago
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    and when you multiply them together its -16

  34. anonymous
    • one year ago
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    yeah

  35. Anguyennn
    • one year ago
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    multiplied with -2 is 32

  36. anonymous
    • one year ago
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    sorry for the mistake :P

  37. Anguyennn
    • one year ago
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    am i correct? haha

  38. Anguyennn
    • one year ago
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    its ok!!! :)

  39. anonymous
    • one year ago
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    yeah ur right

  40. Anguyennn
    • one year ago
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    so would the answer be -20x^2+3x+33

  41. anonymous
    • one year ago
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    Yep but should the x one be -3x?

  42. anonymous
    • one year ago
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    yeah its -3x

  43. Anguyennn
    • one year ago
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    how?

  44. anonymous
    • one year ago
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    other than that your right, good job

  45. anonymous
    • one year ago
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    in last brackets 4x - x = 3x as theres a negative in front it becomes -3x

  46. anonymous
    • one year ago
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    in front of the brackets

  47. Anguyennn
    • one year ago
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    im confused

  48. Anguyennn
    • one year ago
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    I got -x+4x

  49. Anguyennn
    • one year ago
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    which gives you 3

  50. anonymous
    • one year ago
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    You have -(x+2)(2x-1) this becomes -(2x^2-x+4x-2) multiplying everyhting by -1 it becomes -2x^2 +x -4x +2 =-2x^2-3x+2

  51. Anguyennn
    • one year ago
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    why did you multiply everything by -1

  52. anonymous
    • one year ago
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    when you have brackets and a number outside like a(b+x) , to expand you multiply b and x by a. Outside those brackets theres a -, this just means -1*(2x^2-x+4x-2), therefore everything is multiplied by -1.

  53. Anguyennn
    • one year ago
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    ohhhh ok i get it now

  54. anonymous
    • one year ago
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    Ok cool

  55. Anguyennn
    • one year ago
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    so the answer would now be -20x^2-3x+37

  56. anonymous
    • one year ago
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    yep :)

  57. Anguyennn
    • one year ago
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    since you are helping me do you mind helping me with one more math question? please and thank you

  58. anonymous
    • one year ago
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    Ok if you want

  59. Anguyennn
    • one year ago
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    so now its factoring polynomial expressions and it asks to factor by finding the greatest common factor. and the expression is 12x^2y^2-18x^3y+24x^2y

  60. Anguyennn
    • one year ago
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    Thank you for your help

  61. Anguyennn
    • one year ago
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    I appreciate it

  62. anonymous
    • one year ago
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    Ok now factoring is just the reverse of the expanding thing I showed you. Expanding is when you have a number multiplied against brackets and then bringing it all out into a polynomial. Factoring is when you have a plynomial and you turn it into a brackets multiplied against a number.

  63. anonymous
    • one year ago
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    You're very welcome btw, im glad to help

  64. Anguyennn
    • one year ago
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    so could you help me go through this question step by step so that i will get a hang of it please

  65. anonymous
    • one year ago
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    Ok

  66. anonymous
    • one year ago
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    First you have to find one number that exist in all 3 terms.

  67. anonymous
    • one year ago
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    all the terms have x^2 right?

  68. anonymous
    • one year ago
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    the middle one is just X^2 x X

  69. anonymous
    • one year ago
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    to get X^3

  70. anonymous
    • one year ago
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    however the highest y power is only 1 two have y^1 and one has y^2

  71. Anguyennn
    • one year ago
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    this middle one is different

  72. anonymous
    • one year ago
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    all the terms have a multiple of 6, 6 x 2 = 12 6 x 3 = 18 6 x 4 = 24

  73. Anguyennn
    • one year ago
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    yes

  74. anonymous
    • one year ago
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    Ok those are the common factors, you have to find the highest multiple of every variable (in this case x and y) and the highest multiple of the coefficents

  75. anonymous
    • one year ago
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    This means that we can multiply (x^2)(y)(6) by different things to get all the terms

  76. anonymous
    • one year ago
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    Does that make sense?

  77. Anguyennn
    • one year ago
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    just a little bit

  78. anonymous
    • one year ago
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    Ok you will get it better in the next step.

  79. Anguyennn
    • one year ago
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    where did you get 6 from?

  80. anonymous
    • one year ago
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    Now that we have the highest common factor, we have to find what these multiply against to get each term.

  81. Anguyennn
    • one year ago
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    oh 6 is the common factor

  82. anonymous
    • one year ago
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    The 6 is the highest factor of the coeffeicents of each term, it multiplies to make 12 18 and 24

  83. Anguyennn
    • one year ago
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    yes

  84. anonymous
    • one year ago
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    Ok (x^2)(y)(6) * (a+b+c) = the original expression you gave me

  85. anonymous
    • one year ago
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    what does (x^2)(y)6 times against to make 12x^2y^2 ?

  86. anonymous
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    ?

  87. Anguyennn
    • one year ago
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    wait what

  88. Anguyennn
    • one year ago
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    12?

  89. anonymous
    • one year ago
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    6(x^2)(y) is the common factor (highest), this means that it can times against a number to make each of the terms

  90. anonymous
    • one year ago
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    6 x 2 makes 12

  91. anonymous
    • one year ago
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    so the coeffcient must be 2

  92. anonymous
    • one year ago
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    x^2 x 1 = x^2 , we dont worry about this one

  93. anonymous
    • one year ago
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    y x (y ) = y^2

  94. Anguyennn
    • one year ago
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    are you looking at 12x^2y^2 only?

  95. Anguyennn
    • one year ago
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    I am confused to which section of the expression you are explaining to me

  96. anonymous
    • one year ago
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    So the number that 6y(x^2) multiplies agasint to make 12x^2y^2 is 2y

  97. anonymous
    • one year ago
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    we are taking each term 1 by 1

  98. anonymous
    • one year ago
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    This seems a bit tedious, ill make an easier example so you understand whats going on ok?

  99. Anguyennn
    • one year ago
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    yes please

  100. anonymous
    • one year ago
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    Ok lets say we have ab + ac

  101. anonymous
    • one year ago
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    We want to turn it into a bracket times a number

  102. Anguyennn
    • one year ago
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    ok

  103. anonymous
    • one year ago
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    the highest common factor in each term is a

  104. Anguyennn
    • one year ago
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    correct

  105. anonymous
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    That goes outside the bracket

  106. anonymous
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    Now we find the 2 numbers that a multiplies agasint to make ac and ab

  107. anonymous
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    these go inside the brackets

  108. Anguyennn
    • one year ago
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    so would it look like 2a(b+c)?

  109. anonymous
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    just a(b+c)

  110. anonymous
    • one year ago
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    no if you expand it you get a x b + a x c

  111. anonymous
    • one year ago
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    which is ab + ac, what we originally had, this is pretty much what factoring is

  112. anonymous
    • one year ago
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    Makes sense?

  113. Anguyennn
    • one year ago
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    yes

  114. anonymous
    • one year ago
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    ok cool, lets try a harder one then we'll go back to the other

  115. anonymous
    • one year ago
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    lets say 2ab+a^2

  116. anonymous
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    give it a go

  117. anonymous
    • one year ago
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    u there?

  118. Anguyennn
    • one year ago
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    hold on

  119. Anguyennn
    • one year ago
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    i am just looking it over

  120. anonymous
    • one year ago
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    k

  121. anonymous
    • one year ago
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    Remember highest common factor outside brackets, inside goes what it multiplies against to make the orignal terms

  122. Anguyennn
    • one year ago
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    would it be a?

  123. anonymous
    • one year ago
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    yep

  124. Anguyennn
    • one year ago
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    what would the expression look like though?

  125. anonymous
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    a((what a times against to make 2ab) + (what a times against to make a^2))

  126. anonymous
    • one year ago
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    All you're doing is just taking the common factor out leaving everyhting else behind.

  127. Anguyennn
    • one year ago
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    okk!!!

  128. Anguyennn
    • one year ago
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    ok so for 12x^2y^2 you are dividing 12 by 6 am i correct?

  129. anonymous
    • one year ago
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    Yep :)

  130. anonymous
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    you also divide by x^2 and y

  131. Anguyennn
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    and then what is the next step?

  132. anonymous
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    Like this (12x^2y^2)/(6(x^2)y)

  133. anonymous
    • one year ago
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    You get 2y when yo do that

  134. anonymous
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    That is the number which 6(x^2)y times against to make 12x^2y^2 becasue 6(x^2)y * 2y = 12(x^2)(y^)

  135. anonymous
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    (y^2)************

  136. anonymous
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    do the same for the other 2 terms

  137. Anguyennn
    • one year ago
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    where did the squared go for the y?

  138. Anguyennn
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    isn't it suppose to be 6(x^2y^2) ?

  139. anonymous
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    (y^2)/y = y when you divide variables you minus the power of the bottom one from the power of the top one (aslong they are the same variable)

  140. anonymous
    • one year ago
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    for 12x^2y^2 / 6(x^2)y you split it into 3 parts 12/6 = 2 (x^2)/(x^2) = 1 (y^2)/y = y 2 x 1 x y = 2y

  141. Anguyennn
    • one year ago
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    so how come you didn't do (x^2)/x?

  142. anonymous
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    it was (x^2)/(x^2) as (x^2) is the highest common factor

  143. anonymous
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    which is just 1

  144. anonymous
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    you divide all 3 terms by 6(x^2)y which is the highest common factor to get the number the highest common factor times agasint to get those terms

  145. Anguyennn
    • one year ago
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    the expression in the middle in x^3 but the other two is x^2 so x^2 is the common factor because there are more of them?

  146. anonymous
    • one year ago
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    X^3 is just x*x*x X^2 is x*x, the highest is x*x becasue x*x*x is not a factor of the ones with x*x, its bigger than it. x*x can fit into all of them

  147. anonymous
    • one year ago
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    https://www.mathsisfun.com/algebra/factoring.html

  148. anonymous
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    Look at that

  149. Anguyennn
    • one year ago
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    hold on i am looking at the website

  150. Anguyennn
    • one year ago
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    would the whole answer be 2y-3x+12

  151. anonymous
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    Yes that is right

  152. anonymous
    • one year ago
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    Now you got it!

  153. anonymous
    • one year ago
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    Just do some practice and you'll be sweet.

  154. Anguyennn
    • one year ago
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    do you have to put 6x^2y(2y-3x+12) or just 2y-3x+12?

  155. anonymous
    • one year ago
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    Its has to be 6x^2y(2y-3x+12) because remember you turned it into a number times brackets. You can check your answer by expanding, if you get the original expression then its right.

  156. Anguyennn
    • one year ago
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    oh yes it is

  157. Anguyennn
    • one year ago
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    wow thank you so much!!!!!!!!!!!!!!!!!!!!

  158. Anguyennn
    • one year ago
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    thanks for helping me so much it really helped me, now i understand the concept so much

  159. anonymous
    • one year ago
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    You are welcome :) As long as I teach you something I'll be happy. Good luck for any test you have.

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