# How do you multiply (x-6)(x+4)(x+8)?

Apr 23, 2015

$\left(x - 6\right) \left(x + 4\right) \left(x + 8\right)$

$= \left\{\left(x - 6\right) \left(x + 4\right)\right\} \left(x + 8\right)$

We use the Distributive Property of Multiplication or FOIL method to solve the product in the curly brackets

$= \left\{x \cdot x + x \cdot 4 - 6 \cdot x - 6 \cdot 4\right\} \left(x + 8\right)$

$= \left\{{x}^{2} + 4 x - 6 x - 24\right\} \left(x + 8\right)$

$= \left\{{x}^{2} - 2 x - 24\right\} \left(x + 8\right)$

We again use the Distributive Property of Multiplication or FOIL method to solve the product above

$= {x}^{2} \cdot x + {x}^{2} \cdot 8 - \left(2 x\right) \cdot x - \left(2 x\right) \cdot 8 - 24 \cdot x - 24 \cdot 8$

$= {x}^{3} + 8 {x}^{2} - 2 {x}^{2} - 16 x - 24 x - 192$

color(green)( = x^3 +6x^2 - 40x - 192

$\left(x - 6\right) \left(x + 4\right) \left(x + 8\right) = \left(6 - 6\right) \left(6 + 4\right) \left(6 + 8\right) = 0$
${x}^{3} + 6 {x}^{2} - 40 x - 192$
$= {6}^{3} + 6 \left({6}^{2}\right) - 40 \cdot 6 - 192 = 216 + 216 - 240 - 192 = 0$