Question

50 POINTS!

Add or subtract algebraically.

a. (3w² + 17w) + (12w² - 3w)

b. (-14 + 3p² + 2p) - (-5p + 10 - 7p²)

c. (6a² + 2a - 2) + (-7a² + 4a + 11)

I missed a few months of class, so I haven't really learned the basic concepts. It would be awesome if you could explain each step!

Answer 1

To solve this we need to use these formulas:

`(a+b)+(c+d)=a+b+c+d\\(a+b)-(c+d)=a+b-c-d\\(a+b)-(c-d)=a+b-c+d`

`a. \:(3w^2 + 17w) + (12w^2 - 3w)=3w^2 + 17w + 12w^2 - 3w=15w^2+14w\\\\b.\: (-14 + 3p^2 + 2p) - (-5p + 10 - 7p^2)=-14 + 3p^2 + 2p +5p - 10 + 7p^2=\\=10p^2+7p-24\\\\c.\: (6a^2 + 2a - 2) + (-7a^2 + 4a + 11)=6a^2 + 2a - 2-7a^2 + 4a + 11=\\=-a^2+6a+9`

Answer 2

Heya!

Steps to solve:

(3w² + 17w) + (12w² - 3w)

~Remove parenthesis

3w² + 17w + 12w² - 3w

~Combine like terms

(3w²+ 12w²) + (17w - 3w)

~Simplify

15w² + 14w

Steps to solve:

(-14 + 3p² + 2p) - (-5p + 10 - 7p²)

~Remove parenthesis (Multiply "-" to all the numbers on the right parenthesis since there is a subtraction sign outside the parenthesis).

-14 + 3p² + 2p - 5p - 10 + 7p²

~Combine like terms

(3p² + 7p²) + (2p + 5p) + (-14 - 10)

~Simplify

10p² + 7p - 24

Steps to solve:

(6a² + 2a - 2) + (-7a² + 4a + 11)

~Remove parenthesis

6a² + 2a - 2 - 7a² + 4a + 11

~Combine like terms

(6a² - 7a²) + (2a + 4a) + (-2 + 11)

~Simplify

-a² + 6a + 9

Best of Luck!