# How do you simplify (x + 3)(x - 4)(x - 5)?

Apr 3, 2017

${x}^{3} - 6 {x}^{2} - 7 x + 60$

#### Explanation:

To expand a product of factors in the form.

$\left(x + a\right) \left(x + b\right) \left(x + c\right)$

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

$\text{here " a=3,b=-4" and } c = - 5$

$\Rightarrow \left(x + 3\right) \left(x - 4\right) \left(x - 5\right)$

$= {x}^{3} + \left(3 - 4 - 5\right) {x}^{2} + \left(- 12 + 20 - 15\right) x + 60$

$= {x}^{3} - 6 {x}^{2} - 7 x + 60$