Anguyennn
  • Anguyennn
Could someone please help me simplify 3-2(3x-4)(3x+4)-(x+2)(2x-1)?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Do you know the foil rule for expanding brackets?
Anguyennn
  • Anguyennn
yes so I got 3-2(9x^2+12x-12x+16)-(2x^2-x+4x-2) is that correct?
anonymous
  • anonymous
Yep thats right, now just times the number outside the brackets by everything inside.

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anonymous
  • anonymous
Simplify the inside of the brackets firstb to make it easier
Anguyennn
  • Anguyennn
do you minus 3-2 first? .....so it would be 1(9x^2+12x-12x+16)-(2x^2-x+4x-2)?
Anguyennn
  • Anguyennn
oh
Anguyennn
  • Anguyennn
(9x^2+16)-(2x^2+3x-2)
anonymous
  • anonymous
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
anonymous
  • anonymous
yeah what you did was right
Anguyennn
  • Anguyennn
ok now do I multiply the first bracket with -2?
anonymous
  • anonymous
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
anonymous
  • anonymous
onceyou multiply the bracket by -2 you can start combining like terms (same power of x)
Anguyennn
  • Anguyennn
but what about the 3?
Anguyennn
  • Anguyennn
on the outside?
anonymous
  • anonymous
leave that to last, you can only combine it with other numbers by itself (not multiplied by an x)
Anguyennn
  • Anguyennn
so right now I am getting 3(-18x^2+32)-(2x^2-x+4x-2)
anonymous
  • anonymous
just leave the 3, and you forgot about the x in the first bracket
Anguyennn
  • Anguyennn
but it cancels out doesn't it? because 12x-12x is 0
anonymous
  • anonymous
oh yeah true that i forgot :P
Anguyennn
  • Anguyennn
haha its ok
anonymous
  • anonymous
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
anonymous
  • anonymous
Now combine like terms
anonymous
  • anonymous
i make a mistake
anonymous
  • anonymous
it should be -32
anonymous
  • anonymous
on the last line (i screwed up a couple of lines up)
Anguyennn
  • Anguyennn
no its positive
Anguyennn
  • Anguyennn
its +32
anonymous
  • anonymous
-2 x 16 = -32
Anguyennn
  • Anguyennn
-2x-16=32
anonymous
  • anonymous
of i see what was wrong
Anguyennn
  • Anguyennn
because at the beginning its (3x-4)(3x+4)
anonymous
  • anonymous
i accidentaly put +16 when it was -16
Anguyennn
  • Anguyennn
and when you multiply them together its -16
anonymous
  • anonymous
yeah
Anguyennn
  • Anguyennn
multiplied with -2 is 32
anonymous
  • anonymous
sorry for the mistake :P
Anguyennn
  • Anguyennn
am i correct? haha
Anguyennn
  • Anguyennn
its ok!!! :)
anonymous
  • anonymous
yeah ur right
Anguyennn
  • Anguyennn
so would the answer be -20x^2+3x+33
anonymous
  • anonymous
Yep but should the x one be -3x?
anonymous
  • anonymous
yeah its -3x
Anguyennn
  • Anguyennn
how?
anonymous
  • anonymous
other than that your right, good job
anonymous
  • anonymous
in last brackets 4x - x = 3x as theres a negative in front it becomes -3x
anonymous
  • anonymous
in front of the brackets
Anguyennn
  • Anguyennn
im confused
Anguyennn
  • Anguyennn
I got -x+4x
Anguyennn
  • Anguyennn
which gives you 3
anonymous
  • anonymous
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
Anguyennn
  • Anguyennn
why did you multiply everything by -1
anonymous
  • anonymous
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.
Anguyennn
  • Anguyennn
ohhhh ok i get it now
anonymous
  • anonymous
Ok cool
Anguyennn
  • Anguyennn
so the answer would now be -20x^2-3x+37
anonymous
  • anonymous
yep :)
Anguyennn
  • Anguyennn
since you are helping me do you mind helping me with one more math question? please and thank you
anonymous
  • anonymous
Ok if you want
Anguyennn
  • Anguyennn
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
Anguyennn
  • Anguyennn
Thank you for your help
Anguyennn
  • Anguyennn
I appreciate it
anonymous
  • anonymous
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.
anonymous
  • anonymous
You're very welcome btw, im glad to help
Anguyennn
  • Anguyennn
so could you help me go through this question step by step so that i will get a hang of it please
anonymous
  • anonymous
Ok
anonymous
  • anonymous
First you have to find one number that exist in all 3 terms.
anonymous
  • anonymous
all the terms have x^2 right?
anonymous
  • anonymous
the middle one is just X^2 x X
anonymous
  • anonymous
to get X^3
anonymous
  • anonymous
however the highest y power is only 1 two have y^1 and one has y^2
Anguyennn
  • Anguyennn
this middle one is different
anonymous
  • anonymous
all the terms have a multiple of 6, 6 x 2 = 12 6 x 3 = 18 6 x 4 = 24
Anguyennn
  • Anguyennn
yes
anonymous
  • anonymous
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
anonymous
  • anonymous
This means that we can multiply (x^2)(y)(6) by different things to get all the terms
anonymous
  • anonymous
Does that make sense?
Anguyennn
  • Anguyennn
just a little bit
anonymous
  • anonymous
Ok you will get it better in the next step.
Anguyennn
  • Anguyennn
where did you get 6 from?
anonymous
  • anonymous
Now that we have the highest common factor, we have to find what these multiply against to get each term.
Anguyennn
  • Anguyennn
oh 6 is the common factor
anonymous
  • anonymous
The 6 is the highest factor of the coeffeicents of each term, it multiplies to make 12 18 and 24
Anguyennn
  • Anguyennn
yes
anonymous
  • anonymous
Ok (x^2)(y)(6) * (a+b+c) = the original expression you gave me
anonymous
  • anonymous
what does (x^2)(y)6 times against to make 12x^2y^2 ?
anonymous
  • anonymous
?
Anguyennn
  • Anguyennn
wait what
Anguyennn
  • Anguyennn
12?
anonymous
  • anonymous
6(x^2)(y) is the common factor (highest), this means that it can times against a number to make each of the terms
anonymous
  • anonymous
6 x 2 makes 12
anonymous
  • anonymous
so the coeffcient must be 2
anonymous
  • anonymous
x^2 x 1 = x^2 , we dont worry about this one
anonymous
  • anonymous
y x (y ) = y^2
Anguyennn
  • Anguyennn
are you looking at 12x^2y^2 only?
Anguyennn
  • Anguyennn
I am confused to which section of the expression you are explaining to me
anonymous
  • anonymous
So the number that 6y(x^2) multiplies agasint to make 12x^2y^2 is 2y
anonymous
  • anonymous
we are taking each term 1 by 1
anonymous
  • anonymous
This seems a bit tedious, ill make an easier example so you understand whats going on ok?
Anguyennn
  • Anguyennn
yes please
anonymous
  • anonymous
Ok lets say we have ab + ac
anonymous
  • anonymous
We want to turn it into a bracket times a number
Anguyennn
  • Anguyennn
ok
anonymous
  • anonymous
the highest common factor in each term is a
Anguyennn
  • Anguyennn
correct
anonymous
  • anonymous
That goes outside the bracket
anonymous
  • anonymous
Now we find the 2 numbers that a multiplies agasint to make ac and ab
anonymous
  • anonymous
these go inside the brackets
Anguyennn
  • Anguyennn
so would it look like 2a(b+c)?
anonymous
  • anonymous
just a(b+c)
anonymous
  • anonymous
no if you expand it you get a x b + a x c
anonymous
  • anonymous
which is ab + ac, what we originally had, this is pretty much what factoring is
anonymous
  • anonymous
Makes sense?
Anguyennn
  • Anguyennn
yes
anonymous
  • anonymous
ok cool, lets try a harder one then we'll go back to the other
anonymous
  • anonymous
lets say 2ab+a^2
anonymous
  • anonymous
give it a go
anonymous
  • anonymous
u there?
Anguyennn
  • Anguyennn
hold on
Anguyennn
  • Anguyennn
i am just looking it over
anonymous
  • anonymous
k
anonymous
  • anonymous
Remember highest common factor outside brackets, inside goes what it multiplies against to make the orignal terms
Anguyennn
  • Anguyennn
would it be a?
anonymous
  • anonymous
yep
Anguyennn
  • Anguyennn
what would the expression look like though?
anonymous
  • anonymous
a((what a times against to make 2ab) + (what a times against to make a^2))
anonymous
  • anonymous
All you're doing is just taking the common factor out leaving everyhting else behind.
Anguyennn
  • Anguyennn
okk!!!
Anguyennn
  • Anguyennn
ok so for 12x^2y^2 you are dividing 12 by 6 am i correct?
anonymous
  • anonymous
Yep :)
anonymous
  • anonymous
you also divide by x^2 and y
Anguyennn
  • Anguyennn
and then what is the next step?
anonymous
  • anonymous
Like this (12x^2y^2)/(6(x^2)y)
anonymous
  • anonymous
You get 2y when yo do that
anonymous
  • anonymous
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^)
anonymous
  • anonymous
(y^2)************
anonymous
  • anonymous
do the same for the other 2 terms
Anguyennn
  • Anguyennn
where did the squared go for the y?
Anguyennn
  • Anguyennn
isn't it suppose to be 6(x^2y^2) ?
anonymous
  • anonymous
(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)
anonymous
  • anonymous
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
Anguyennn
  • Anguyennn
so how come you didn't do (x^2)/x?
anonymous
  • anonymous
it was (x^2)/(x^2) as (x^2) is the highest common factor
anonymous
  • anonymous
which is just 1
anonymous
  • anonymous
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
Anguyennn
  • Anguyennn
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?
anonymous
  • anonymous
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
anonymous
  • anonymous
https://www.mathsisfun.com/algebra/factoring.html
anonymous
  • anonymous
Look at that
Anguyennn
  • Anguyennn
hold on i am looking at the website
Anguyennn
  • Anguyennn
would the whole answer be 2y-3x+12
anonymous
  • anonymous
Yes that is right
anonymous
  • anonymous
Now you got it!
anonymous
  • anonymous
Just do some practice and you'll be sweet.
Anguyennn
  • Anguyennn
do you have to put 6x^2y(2y-3x+12) or just 2y-3x+12?
anonymous
  • anonymous
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.
Anguyennn
  • Anguyennn
oh yes it is
Anguyennn
  • Anguyennn
wow thank you so much!!!!!!!!!!!!!!!!!!!!
Anguyennn
  • Anguyennn
thanks for helping me so much it really helped me, now i understand the concept so much
anonymous
  • anonymous
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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