# How do you multiply (a+2) (a^2- 3a+7)?

Jul 27, 2015

=color(blue)(a^3 -a^2 +a+14

#### Explanation:

color(blue)((a+2))(a^2−3a+7)

Here, we need to multiply each term within first bracket with the three terms of the second bracket.

=color(blue)((a))(a^2−3a+7))+ color(blue)((2))(a^2−3a+7)

$= {a}^{3} - 3 {a}^{2} + 7 a + 2 {a}^{2} - 6 a + 14$

grouping like terms

$= {a}^{3} + \left(2 {a}^{2} - 3 {a}^{2}\right) + \left(7 a - 6 a\right) + 14$
=color(blue)(a^3 -a^2 +a+14