Frauffshiesiaf6s

2022-01-31

What is the standard form of $y=\left(2+{x}^{2}\right)\left(x-7\right)-{\left(2x+3\right)}^{2}$?

Reagan Blair

Explanation:
the first thing to do is multiply out the pairs of brackets
$\left(2+{x}^{2}\right)\left(x-7\right)=2\left(x-7\right)+{x}^{2}\left(x-7\right)=2x-14+{x}^{3}-7{x}^{2}$
and ${\left(2x+3\right)}^{2}=\left(2x+3\right)\left(2x+3\right)=2x\left(2x+3\right)+3\left(2x+3\right)$
$=4{x}^{2}+6x+6x+9$
expression now becomes
$2x-14+{x}^{3}-7{x}^{2}-\left(4{x}^{2}+12x+9\right)$
$=2x-14+{x}^{3}-7{x}^{2}-4{x}^{2}-12x-9$
$={x}^{3}-11{x}^{2}-10x-23$
Result:
${x}^{3}-11{x}^{2}-10x-23$

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