How do you simplify (x + 9)(x - 2)(x - 7)?

Jun 12, 2017

${x}^{3} - 67 x + 126$

Explanation:

$\text{factors of the form}$

$\left(x + a\right) \left(x + b\right) \left(x + c\right) \text{ may be expanded as}$

${x}^{3} + \left(a + b + c\right) {x}^{2} + \left(a b + b c + a c\right) x + a b c$

$\text{here " a=9,b=-2" and } c = - 7$

$\Rightarrow \left(x + 9\right) \left(x - 2\right) \left(x - 7\right)$

$= {x}^{3} + \left(9 - 2 - 7\right) {x}^{2} + \left(- 18 + 14 - 63\right) x + \left(9 \times - 2 \times - 7\right)$

$= {x}^{3} - 67 x + 126$