# How do you multiply (a + 2)(a^2 - 5a +9)?

Jul 16, 2015

You can use distributivity to find:

$\left(a + 2\right) \left({a}^{2} - 5 a + 9\right) = {a}^{3} - 3 {a}^{2} - a + 18$

#### Explanation:

$\left(a + 2\right) \left({a}^{2} - 5 a + 9\right)$

$= a \left({a}^{2} - 5 a + 9\right) + 2 \left({a}^{2} - 5 a + 9\right)$

$= \left({a}^{3} - 5 {a}^{2} + 9 a\right) + \left(2 {a}^{2} - 10 a + 18\right)$

$= {a}^{3} - 5 {a}^{2} + 2 {a}^{2} + 9 a - 10 a + 18$

$= {a}^{3} + \left(- 5 + 2\right) {a}^{2} + \left(9 - 10\right) a + 18$

$= {a}^{3} - 3 {a}^{2} - a + 18$

Alternatively, look at each power of $a$ in descending order and collect the terms that multiply to contribute to the coefficient of that power of $a$:

${a}^{3}$ : $a \cdot {a}^{2} = {a}^{3}$

${a}^{2}$ : $\left(a \cdot - 5 a\right) + \left(2 \cdot {a}^{2}\right) = - 5 {a}^{2} + 2 {a}^{2} = - 3 {a}^{2}$

$a$ : $\left(a \cdot 9\right) + \left(2 \cdot - 5 a\right) = 9 a - 10 a = - a$

$1$ : $2 \cdot 9 = 18$