# How do you combine like terms in (2a + 3) ^ { 2} + ( a - 5) ^ { 2}?

Jun 9, 2018

$5 {a}^{2} + 2 a + 34$

#### Explanation:

Using the formulas

${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$
${\left(a - b\right)}^{2} = {a}^{2} - 2 a b + {b}^{2}$
we get

$4 {a}^{2} + 9 + 12 a + {a}^{2} - 10 a + 25$
and this is

$5 {a}^{2} + 2 a + 39$

Jun 9, 2018

$5 {a}^{2} + 2 a + 34$

#### Explanation:

First FOIL the squared terms:

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

$= \left(2 a + 3\right) \left(2 a + 3\right) + \left(a - 5\right) \left(a - 5\right)$

$= 4 {a}^{2} + 6 a + 6 a + 9 + {a}^{2} - 5 a - 5 a + 25$

now "combine like terms":

$= 5 {a}^{2} + 2 a + 34$