# How do you evaluate (a + 9) ^ { 2} - ( a - 4) ^ { 2}?

Jan 30, 2018

$26 a + 65$

#### Explanation:

${\left(a + 9\right)}^{2} - {\left(a - 4\right)}^{2}$
$= {a}^{2} + 18 a + {9}^{2} - {a}^{2} + 8 a - {4}^{2}$
$= 18 a + 8 a + 81 - 16$
$= 26 a + 65$

Jan 30, 2018

$26 a + 65$

#### Explanation:

$\text{this is a "color(blue)"difference of squares}$

•color(white)(x)a^2-b^2=(a-b)(a+b)

${\left(a + 9\right)}^{2} - {\left(a - 4\right)}^{2}$

$\text{with "a=a+9" and } b = a - 4$

$= \left(a + 9 - \left(a - 4\right)\right) \left(a + 9 + a - 4\right)$

$= \left(\cancel{a} + 9 \cancel{- a} + 4\right) \left(2 a + 5\right)$

$= 13 \left(2 a + 5\right)$

$= 26 a + 65$