Question

How do you factor `36a^2-48a+16`?

Answer 1

`4(3a - 2)^2`

Explanation:

There is a 'common factor' of 4

hence 4 (`9a^2 - 12a + 4)`

To factor the trinomial: `9 xx 4 = 36`

Consider factors of 36 which also sum to -12

Factors of 36: 1,2,3,4,6,9,12, 18 and 36 ( and their negatives )

The 'pair' which sum to -12 are -6 and -6

so trinomial becomes: `9a^2 - 6a - 6a + 4`

factor in pairs. `[9a^2 - 6a ] and [ -6a + 4 ]`

hence 3a(3a - 2) and -2 (3a - 2 )

There is a common factor of (3a - 2 )

so (3a - 2 )(3a - 2 ) are the factors of the trinomial.

Putting all this together to obtain :

`36a^2 - 48a + 16 = 4 (3a - 2 )^2`