Question

How do you factor `36x^2+96xy+64y^2`?

Answer 1

`4(3x+4y)^2`

Explanation:

`36x^2+96xy+64y^2 = 4(9x^2+24 x y + 16 y^2) = 4(3x+4y)^2`

Answer 2

`36x^2+96xy+64y^2=4(3x+4y)^2`

Explanation:

Note that all of the coefficients are divisible by `4`, so we can separate that out as a scalar factor. Then noticing that the first and last terms are perfect squares, we find that the middle term matches the pattern:

`a^2+2ab+b^2 = (a+b)^2`

with `a=3x` and `b=4y` as follows:

`36x^2+96xy+64y^2`

`=4(9x^2+24xy+16y^2)`

`=4((3x)^2+2(3x)(4y)+(4y)^2)`

`=4(3x+4y)^2`