## sabrinahaley97 2 years ago .

1. satellite73

\[(5x^2 + 3x + 4) − (2x^2 − 6x + 3)\]distribute the minus sign and get \[5x^2 + 3x + 4 -2x^2 + 6x - 3)\]

2. satellite73

since you are only asked for B you job is to compute \(3+6\)

3. satellite73

yes

4. jim_thompson5910

Add up 3x^2 - 9 and 2x + 9 So (3x^2 - 9) + (2x + 9) = ???

5. sabrinahaley97

5x^2 ?

6. jim_thompson5910

Sorry, I didn't see the first x Add x, 3x^2 - 9 and 2x+9 (x) + (3x^2 - 9) + (2x + 9) x + 3x^2 - 9 + 2x + 9 3x^2 + 3x + 0 3x^2 + 3x

7. jim_thompson5910

So after adding x, 3x^2 - 9 and 2x + 9, you will get 3x^2 + 3x, which is the total distance covered

8. sabrinahaley97

soo its 3x^2 + 3x

9. satellite73

add them up \[x+3x^2 - 9+2x + 9\]

10. satellite73

yes

11. sabrinahaley97

thanks!

12. satellite73

they really reach for these "word problems" don't they ?

13. satellite73

they could have said "add the polynomials"

14. sabrinahaley97

LOLLL yess they do !! Can you guys do me onee more favor and just double check my work ?

15. jim_thompson5910

sure, what do you need to check

16. sabrinahaley97

ill write the 5 questions and show you my answers

17. sabrinahaley97

1. Simplify the following expression: (x − 8y) - (2x − 4y)If the final answer is written in the form Ax + By, what is the value of B? 2. Simplify: (4x − 6) − (5x + 1) 3. Simplify: (5x^2 + 3x + 4) + (5x^2 + 5x − 1) 4. Simplify: (4x − 6) + (3x + 6) & You helped me with the other 2 questions so i just put the ones i did on my own but these were my answers 1. 4y 2. -x-7 3. 10x^2 + 8x + 5 4. 7x+12

18. jim_thompson5910

ok one sec

19. sabrinahaley97

alrighty :] Thanks!!

20. jim_thompson5910

#1 the form is form Ax + By they want the value of B, so the answer cannot be 4y

21. jim_thompson5910

besides, -8y + 4y isn't 4y anyway you lost a sign somewhere

22. sabrinahaley97

Im bad with my signs /: negatives and positives -.- so confusing

23. jim_thompson5910

think of it like this -8 + 4 is the same as saying you're 8 dollars in debt, but you paid off \$4 of that debt, so you're now 4 dollars in debt

24. jim_thompson5910

so that explains how -8 + 4 = -4

25. jim_thompson5910

and why -8y + 4y = -4y

26. sabrinahaley97

so itd be -4?

27. jim_thompson5910

B is -4, yep

28. sabrinahaley97

oki

29. jim_thompson5910

# 2 is correct, so congrats on that

30. sabrinahaley97

thanks :]

31. jim_thompson5910

#3 is close

32. jim_thompson5910

but not correct fully

33. jim_thompson5910

4 + (-1) is NOT 5

34. sabrinahaley97

-3?

35. jim_thompson5910

you have 4 dollars you add on 1 IOU

36. jim_thompson5910

you really have 4-1 = 3 dollars left (after you pay off the IOU)

37. jim_thompson5910

so that's why 4 + (-1) = 4 - 1 = 3

38. sabrinahaley97

oh alright ! i get it now.

39. jim_thompson5910

ok great

40. jim_thompson5910

# 4 is also incorrect

41. sabrinahaley97

sorry im blonde it takes a little bit.

42. jim_thompson5910

that's ok, just practice practice practice and hair color is just skin deep...has nothing to do with intelligence

43. sabrinahaley97

Lol yeah , im guessing #4 is 7x-12

44. jim_thompson5910

-6 + 6 = ???

45. jim_thompson5910

-6 means you are \$6 in debt add on \$6, so you are paying off \$6 are you still in debt?

46. sabrinahaley97

nope itd be zero :o

47. jim_thompson5910

yep

48. jim_thompson5910

-6+6 = 0

49. sabrinahaley97

50. jim_thompson5910

so you'd have 7x+0 or just 7x

51. jim_thompson5910

you got it

52. sabrinahaley97

ok aha :]

53. jim_thompson5910

just watch out for the signs and try not to forget any

54. sabrinahaley97

Ill think of the whole dollar thing next time i come to the signs , Thank you so much ! ! :]

55. jim_thompson5910

that's how I grasp negatives when I stumble a bit, and you're welcome

56. sabrinahaley97

Ive always troubled negatives , ive been taking algebra 1 for 3 years now , and havent passed . Im working so much harder now ,

57. jim_thompson5910

have you thought of using money terms for negatives before? I'm just curious how your teachers have taught negatives in the past

58. sabrinahaley97

ive heard of it but it was never enforced.

59. jim_thompson5910

I gotcha, so they brought it up (maybe once or twice), but never really stuck to it

60. sabrinahaley97

nopeeeee

61. sabrinahaley97

Im trying to finish up my work for next week so im ahead so i can spend my spring break with my younger sister , would you mind helping me with Multiplying monomials?

62. jim_thompson5910

sure I can help

63. sabrinahaley97

Choose the correct simplification of the expression d^3 • d^5. d d^15 d^2 d^8

64. jim_thompson5910

what did you get

65. sabrinahaley97

the arrow represents the degree of the monomials incase you didnt already know lol. and i think its d^15??

66. jim_thompson5910

^ means exponents, yes I know and no it's not d^15

67. jim_thompson5910

if you are multiplying expressions with the same base, then you add the corresponding exponents

68. jim_thompson5910

example x^2 times x^3 = x^(2+3) = x^5

69. sabrinahaley97

Alright that sounds a little better so d^8 ?

70. jim_thompson5910

because you can expand out the 'x' terms and you'll see 5 total x terms

71. jim_thompson5910

yep d^8

72. sabrinahaley97

alright you make this so much easier than the lesson lol

73. jim_thompson5910

74. jim_thompson5910

75. sabrinahaley97

Choose the correct simplification of the expression (b^5)^4. b^9 b^625 b^20 b

76. sabrinahaley97

b^20 ?

77. jim_thompson5910

you got ???

78. jim_thompson5910

perfect

79. jim_thompson5910

you're a total pro at this

80. sabrinahaley97

HA i wish!

81. jim_thompson5910

you're just not giving yourself enough credit

82. sabrinahaley97

Choose the correct simplification of the expression (3x)^4. 81x^4 12x^5 81x^5 12x^4

83. jim_thompson5910

raise each piece to the 4th power

84. sabrinahaley97

81x^4 ?

85. jim_thompson5910

so you raise 3 to the 4th power to get ____

86. jim_thompson5910

yep, you got it

87. jim_thompson5910

see you know this stuff

88. sabrinahaley97

haha slowly but getting it !! :)

89. jim_thompson5910

well as long as you get there, that's all that matters

90. sabrinahaley97

Choose the correct simplification of the expression (x^2y)^2. x^4y^3 x^6y^6 x^4y^2 xy^4

91. jim_thompson5910

what did you get

92. sabrinahaley97

Havent even tried it yet lol .but im thinking the ^2 on the outside is going to distribute to the ones in the parenthese?

93. jim_thompson5910

yes that's one way of thinking about it basically you raise each part to the 2nd power

94. jim_thompson5910

x^2 to the 2nd power ----> x^2 * x^2 = x^(2+2) = x^4

95. jim_thompson5910

y to the second power -----> y^2

96. jim_thompson5910

or you can multiply the exponents multiply the outer by each of the inner

97. sabrinahaley97

so x^4y^2

98. jim_thompson5910

yep

99. sabrinahaley97

:] this isnt so hard

100. jim_thompson5910

no, it's not at all just depends on how much practice you have and how you look at it

101. sabrinahaley97

Choose the correct simplification of the expression b^5 • b^4. b b^9 b^20 b^−1

102. jim_thompson5910

you got _____

103. sabrinahaley97

b^9 ?

104. jim_thompson5910

correct

105. sabrinahaley97

:DD !!

106. jim_thompson5910

you add the exponents I'll brb

107. sabrinahaley97

3 more ,

108. sabrinahaley97

ok sounds good.

109. jim_thompson5910

no worries I'll be back in a few min and I'll help you with those 3

110. sabrinahaley97

Okay :D

111. jim_thompson5910

ok back

112. sabrinahaley97

Choose the correct simplification of the expression (d3)^5. d^8 d^15 d^243 d

113. sabrinahaley97

d^15 right ?

114. jim_thompson5910

correct, assuming you mean (d^3)^5

115. sabrinahaley97

yes sorry i forgot the ^ x]

116. jim_thompson5910

no worries

117. sabrinahaley97

okay these last 3 .

118. sabrinahaley97

heres 2 of the 3

119. jim_thompson5910

and you got what for each

120. sabrinahaley97

How do i simplify them ?

121. sabrinahaley97

122. jim_thompson5910

(3d)^3 turns into 27d^3

123. jim_thompson5910

so (3d)^3 * d becomes 27d^3 * d

124. jim_thompson5910

and that becomes what?

125. sabrinahaley97

um. 27d^4 ?

126. jim_thompson5910

good

127. sabrinahaley97

alright i struggled a little bit

128. jim_thompson5910

now simplify the other expression

129. jim_thompson5910

that's ok, just keep practicing it and it'll come more easily to you

130. sabrinahaley97

the second one the exponents are just gonna get added to each other right ?

131. jim_thompson5910

no, when you square something that has an exponent, you are multiplying the exponents

132. jim_thompson5910

ex: (3x^5)^2 ---> 9x^(5*2) = 9x^(10)

133. sabrinahaley97

3d^4

134. jim_thompson5910

so the exponents are different? or equal?

135. sabrinahaley97

equal

136. jim_thompson5910

so that means you go with C for the first one

137. jim_thompson5910

exponents are the same

138. sabrinahaley97

alright number 8 looks like mumbo jumbo...

139. jim_thompson5910

same thing applies to #8, it's just a bit more complicated maybe

140. jim_thompson5910

they want you to simplify as much as possible, then compare exponents for expressions 1 and 2

141. jim_thompson5910

(2y^2)^3 = 8y^(2*3) = 8y^6

142. sabrinahaley97

alright .

143. jim_thompson5910

(y^9)*(2y^2)^3 turns into y^9 * 8y^6

144. sabrinahaley97

145. jim_thompson5910

just added it back in so to speak

146. jim_thompson5910

I focused on simplifying (2y^2)^3 first

147. jim_thompson5910

then re-introduced the y^9 back in

148. sabrinahaley97

okay so the first one you just add the like terms now right?

149. jim_thompson5910

150. sabrinahaley97

y^9 * 8y^6 = 9y^15

151. jim_thompson5910

the exponent is correct, but that 8 should stay the same

152. jim_thompson5910

so it's 8y^15

153. jim_thompson5910

silly typo though

154. sabrinahaley97

alright so 8y^15 for the first one ,

155. jim_thompson5910

now simplify the second one using the same steps

156. jim_thompson5910

(2y^3)^2 = ???

157. sabrinahaley97

4y^6

158. jim_thompson5910

good

159. jim_thompson5910

(9y)(2y^3)^2 becomes 9y*4y^6

160. sabrinahaley97

13y^6

161. jim_thompson5910

you multiply the coefficients out front

162. jim_thompson5910

9*4 = 36

163. jim_thompson5910

and you add the exponents 1+6 = 7

164. sabrinahaley97

so 36y^7 ?

165. jim_thompson5910

yep

166. sabrinahaley97

that one was hard lol

167. jim_thompson5910

now compare 8y^15 to 36y^7

168. jim_thompson5910

its ok, it'll get easier over time

169. sabrinahaley97

the first ones exponents are greater than

170. jim_thompson5910

yep

171. sabrinahaley97

Alright this is my last one .

172. jim_thompson5910

so A

173. sabrinahaley97

thank god

174. jim_thompson5910

lol

175. sabrinahaley97

Part 1: Explain, using complete sentences, how to simplify the expression below. Part 2: What is the simplified expression? (3x^3y^4)(2x^2y^6)

176. jim_thompson5910

the coefficients are 3 and 2 what do you do with these?

177. sabrinahaley97

multiply them

178. jim_thompson5910

good

179. jim_thompson5910

3 * 2 = 6 is your final coefficient

180. jim_thompson5910

now for each variable, you add the corresponding exponents

181. sabrinahaley97

so 6x^5 ?

182. jim_thompson5910

so for the x terms, you add the exponents 3 and 2 to get 3+2 = 5 5 is the final exponent for x

183. jim_thompson5910

so far so good, now do y

184. sabrinahaley97

well y doesnt have any numbers but every variable is equal to 1 , so would it be 2y^10?

185. jim_thompson5910

186. jim_thompson5910

just focus on the exponents for y

187. sabrinahaley97

so y^10 ?

188. jim_thompson5910

they are 4 and 6, they add to 4+6 = 10

189. jim_thompson5910

yep

190. jim_thompson5910

so all together, we get 6x^5y^10

191. sabrinahaley97

alright . so thats the simplied answer?

192. jim_thompson5910

it is

193. sabrinahaley97

that was easier lol

194. jim_thompson5910

lol depends on how you look at it i guess

195. sabrinahaley97

Thank you so much for all your time helping me tonight .

196. jim_thompson5910

you're welcome