# How do you factor 2x ^ { 2} - 5a x + 2a ^ { 2}?

Jun 9, 2018

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

#### Explanation:

$2 {x}^{2} - 5 a x + 2 {a}^{2} = 2 {x}^{2} - 4 a x - a x + 2 {a}^{2}$

$= 2 x \left(x - 2 a\right) - a \left(x - 2 a\right)$

$= \left(x - 2 a\right) \left(2 x - a\right)$ [Ans]

Jun 9, 2018

$\implies \left(2 x - a\right) \left(x - 2 a\right)$

#### Explanation:

$2 {x}^{2} - 5 a x + 2 {a}^{2}$

Split the middle term coefficient (-5) in two such numbers (-4 and -1) so that we get their sum as the middle term and product (-4 x -1)as the product of first term and last term coefficients (2 x 2 =4) and rewrite:

$2 {x}^{2} - 4 a x - 1 a x + 2 {a}^{2}$

$\implies 2 x \left(x - 2 a\right) - 1 a \left(x - 2 a\right)$

$\implies \left(2 x - 1 a\right) \left(x - 2 a\right)$

So the factors are : $\left(2 x - a\right) \mathmr{and} \left(x - 2 a\right)$