Question

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

Explanation:

Step1: Simplify the first option

\[

$$\begin{align*} (-17x^{2}+2x - 3)+(2x^{2}-31x - 9)&=(-17x^{2}+2x^{2})+(2x-31x)+(-3 - 9)\\ &=-15x^{2}-29x - 12 \end{align*}$$

\]

Step2: Simplify the second option

\[

$$\begin{align*} -2(7x + 1)-5(3x^{2}+3x + 2)&=-14x-2-(15x^{2}+15x + 10)\\ &=-15x^{2}-29x - 12 \end{align*}$$

\]

Step3: Simplify the third option

\[

$$\begin{align*} (-7x^{2}-21x + 13)-(8x^{2}+8x + 25)&=-7x^{2}-21x + 13-8x^{2}-8x - 25\\ &=-15x^{2}-29x - 12 \end{align*}$$

\]

Step4: Simplify the fourth option

\[

$$\begin{align*} (5x^{2}-10x + 8)-(10x^{2}+19x + 20)&=5x^{2}-10x + 8-10x^{2}-19x - 20\\ &=-5x^{2}-29x - 12 \end{align*}$$

\]

Step5: Simplify the fifth option

\[

$$\begin{align*} -2(4x - 15)-3(5x^{2}+7x + 6)&=-8x + 30-(15x^{2}+21x + 18)\\ &=-15x^{2}-29x + 12 \end{align*}$$

\]

Step6: Simplify the sixth option

\[

$$\begin{align*} (-19x^{2}-4x - 7)+(4x^{2}+25x - 5)&=(-19x^{2}+4x^{2})+(-4x+25x)+(-7 - 5)\\ &=-15x^{2}+21x - 12 \end{align*}$$

\]

Answer:

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