# How do you write (x + 7)(x – 3)(x – 2) in standard form?

Apr 18, 2016

$= {x}^{3} + 2 {x}^{2} - 29 x + 42$

#### Explanation:

This is a long one, but an easy one once you know this property: $\left(a + b\right) \left(c + d\right) = a \left(c + d\right) + b \left(c + d\right) = a b + a d + b c + b d$.
First lets ignore the $\left(x - 2\right)$, and just expand the $\left(x + 7\right) \left(x - 3\right)$
$\left(x + 7\right) \left(x - 3\right) \left(x - 2\right) = \left(x - 2\right) \cdot \left(x + 7\right) \left(x - 3\right)$

$= \left(x - 2\right) \cdot \left({x}^{2} - 3 x + 7 x - 21\right)$

$= \left(x - 2\right) \cdot \left({x}^{2} + 4 x - 21\right)$

$= x \left({x}^{2} + 4 x - 21\right) - 2 \left({x}^{2} + 4 x - 21\right)$

$= {x}^{3} + 4 {x}^{2} - 21 x - 2 {x}^{2} - 8 x + 42$

$= {x}^{3} + 2 {x}^{2} - 29 x + 42$