How do you find the product of (9 - 7x)^2 ?

Mar 8, 2018

$81 - 126 x + 49 {x}^{2}$

Explanation:

$\text{note } {\left(9 - 7 x\right)}^{2} = \left(9 - 7 x\right) \left(9 - 7 x\right)$

$\text{each term in the second factor must be multiplied by}$
$\text{each term in the first factor}$

$\Rightarrow \left(\textcolor{red}{9 - 7 x}\right) \left(9 - 7 x\right)$

$= \textcolor{red}{9} \left(9 - 7 x\right) \textcolor{red}{- 7 x} \left(9 - 7 x\right)$

$= \left(\textcolor{red}{9} \times 9\right) + \left(\textcolor{red}{9} \times - 7 x\right) + \left(\textcolor{red}{- 7 x} \times 9\right) + \left(\textcolor{red}{- 7 x} \times - 7 x\right)$

$= 81 \textcolor{b l u e}{- 63 x} \textcolor{b l u e}{- 63 x} + 49 {x}^{2}$

$= 81 - 126 x + 49 {x}^{2}$