Question

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

Answer 1

`2 x^2-5 a x+ 2 a^2 =(x-2 a)(2 x -a)`

Explanation:

`2 x^2-5 a x+ 2 a^2 = 2 x^2-4 a x - a x+ 2 a^2`

`= 2 x (x-2 a) - a( x- 2 a)`

`= (x-2 a)(2 x -a)` [Ans]

Answer 2

`=> (2x-a)(x-2a)`

Explanation:

`2x ^ { 2} - 5a x + 2a ^ { 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:

`2x ^ { 2} - 4a x -1 ax + 2a ^ { 2}`

`=> 2x (x - 2a) -1a (x- 2a)`

`=> (2x-1a)(x-2a)`

So the factors are : `(2x-a) and (x-2a)`