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webwork / hs rowe cpma / 5.4 introduction to polynomials / 6
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5.4 introduction to polynomials: pro
(1 point)
the expression $2(6x^{2}+6x + 6)-3(6x^{2}+7x + 4)$ equals
$\square x^{2}+\square x+\square$
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Explanation:

Step1: Expand the expressions

$$\begin{align*} 2(6x^{2}+6x + 6)&=2\times6x^{2}+2\times6x+2\times6=12x^{2}+12x + 12\\ -3(6x^{2}+7x + 4)&=-3\times6x^{2}-3\times7x-3\times4=-18x^{2}-21x-12 \end{align*}$$

Step2: Combine like - terms

$$\begin{align*} &(12x^{2}+12x + 12)+(-18x^{2}-21x-12)\\ =&(12x^{2}-18x^{2})+(12x-21x)+(12 - 12)\\ =&-6x^{2}-9x+0 \end{align*}$$

Answer:

$-6x^{2}-9x+0$