# How do you find the product of (n-4)(n+2)(n+1)?

Apr 2, 2017

${n}^{3} - {n}^{2} - 10 n - 8$

#### Explanation:

$\text{Given factors of the form } \left(n + a\right) \left(n + b\right) \left(n + c\right)$

$\text{We can expand using the method}$

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

$\text{here " a=-4,b=2} \mathmr{and} c = 1$

$\Rightarrow {n}^{3} + \left(- 4 + 2 + 1\right) {n}^{2} + \left(- 8 + 2 - 4\right) n + \left(- 4 \times 2 \times 1\right)$

$= {n}^{3} - {n}^{2} - 10 n - 8 \leftarrow \textcolor{red}{\text{ is the product}}$