Question

select all the expressions that are equivalent to the polynomial below.
$-15x^2 - 29x - 12$
$square$ $(5x^2 - 10x + 8) - (10x^2 + 19x + 20)$
$square$ $-2(4x - 15) - 3(5x^2 + 7x + 6)$
$square$ $(-17x^2 + 2x - 3) + (2x^2 - 31x - 9)$
$square$ $-2(7x + 1) - 5(3x^2 + 3x + 2)$
$square$ $(-7x^2 - 21x + 13) - (8x^2 + 8x + 25)$
$square$ $(-19x^2 - 4x - 7) + (4x^2 + 25x - 5)$

Explanation:

Step1: Simplify first expression

Remove parentheses, combine like terms:
$(5x^2 - 10x + 8) - (10x^2 + 19x + 20) = 5x^2 -10x +8 -10x^2 -19x -20 = -5x^2 -29x -12$

Step2: Simplify second expression

Distribute coefficients, combine like terms:
$-2(4x - 15) - 3(5x^2 + 7x + 6) = -8x +30 -15x^2 -21x -18 = -15x^2 -29x +12$

Step3: Simplify third expression

Remove parentheses, combine like terms:
$(-17x^2 + 2x - 3) + (2x^2 - 31x - 9) = -17x^2 +2x -3 +2x^2 -31x -9 = -15x^2 -29x -12$

Step4: Simplify fourth expression

Distribute coefficients, combine like terms:
$-2(7x + 1) - 5(3x^2 + 3x + 2) = -14x -2 -15x^2 -15x -10 = -15x^2 -29x -12$

Step5: Simplify fifth expression

Remove parentheses, combine like terms:
$(-7x^2 - 21x + 13) - (8x^2 + 8x + 25) = -7x^2 -21x +13 -8x^2 -8x -25 = -15x^2 -29x -12$

Step6: Simplify sixth expression

Remove parentheses, combine like terms:
$(-19x^2 - 4x - 7) + (4x^2 + 25x - 5) = -19x^2 -4x -7 +4x^2 +25x -5 = -15x^2 +21x -12$

Answer:

$\boldsymbol{(-17x^2 + 2x - 3) + (2x^2 - 31x - 9)}$
$\boldsymbol{-2(7x + 1) - 5(3x^2 + 3x + 2)}$
$\boldsymbol{(-7x^2 - 21x + 13) - (8x^2 + 8x + 25)}$