Hiya. I have 7 expressions that I have been asked to simplify. I worked all of them out, and if you could, I'd like you to check my work for me.

Question

Here they are:

1. (x^2 + 3x - 9) + (-4x^2 + 2x - 3)

My answer: -4x^4 + 5x - 12

2. (x - 2)(3x + 5)

My answer: 3x^2 - 30x - 10

3. (r + 3)^2

My answer: r^2 + 6r + 9

4. (p^2 + 4p - 23) - (3p^2 - 23p - 23)

My answer: 3p^4 - 19p - 46

5. (5z - 2)(5z + 2)

My answer: 25z^4 - 4

6. (2m - 4)(m^2 + 2m + 4)

My answer: 2m^3

7. (3x - 2)(2x - 3)

My answer: 6x^2 - 13x + 6

I know there were quite a few there, so I really appreciate you helping me out. If I made any mistakes, please let me know what I did wrong so I can correct it. Thank you so much!

Answer 1

1. (x^2 + 3x - 9) + (-4x^2 + 2x - 3)

My answer: -4x^4 + 5x - 12
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my answer, add like terms
x^2 - 4 x^2 = - 3 x^2 for example

-3 x^2 + 5 x -12

Answer 2

2. (x - 2)(3x + 5)

My answer: 3x^2 - 30x - 10
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My answer, either FOIL or use distributive property
FOIL
3 x^2 + 5 x - 6 x -10
= 3 x^2 - x - 10
distributive property
x(3x+5) -2(3x+5)
3 x^2 + 5 x - 6 x - 10 remarkably similar

Answer 3

#1 should be
-3x^2 + 5x- 12

#2
3x^2+ 5x - 6x - 10 = 3x^2- x - 10

#3, good, yeahhh
#4, -2p^2 + 27p
#5, yeahhh
#6 good grief!!!
= 2m^3 + 4m^2 + 8m - 4m^2 - 8m - 16
= 2m^3 - 16

#7, correct

Answer 4

3. (r + 3)^2

My answer: r^2 + 6r + 9 YES

Answer 5

something like 6 use that distributive property
6. (2m - 4)(m^2 + 2m + 4)
2m (m^2 + 2m + 4) = 2 m^3 +4 m^2 + 8 m
-4 (m^2 + 2m + 4) = 0 m^3 -4 m^2 - 8 m -16
-----------------------------------add
2 m^3 -16

Answer 6

Thanks Damon and Reiny for your help!