Question

Factorize the following expressions completely.

6x2y3 +18xy + 3x2y2 + 9x

y2 – x2 + 8y + 16

64x6 – y6

Answer 1

9x4y5+18xy+9x

I think this is the answer to the first one.

Answer 2

Walker's answer is very very wrong!
You cannot add unlike terms.

this is done by grouping
6x2y3 +18xy + 3x2y2 + 9x
= 6x^2y^3 + 3x^2y^2 + 18xy + 9x
= 3x^2y^2(2y + 3) + 9x(2y + 3)
= (2y+3)(3x^2y^2 + 9x)
= x(2y+3)(3xy^2 + 9)

Answer 3

y2 – x2 + 8y + 16 = (y-4)^2 - x^2
= (y-4+x)(y-4-x)

64x^6 - y^6 is also the difference of two squares, and so can be written
(8x^3 -y)(8x^3 + y)
Additional factoring, which is possible, would require fractional powers of y, so I will stop there

Answer 4

I forgot about that. Thank You for correcting me :).