Question

Part A: Factor 3x2y2 − 2xy2 − 8y2. Show your work. (4 points)

Answer 1

Answer:

Check below.

Step-by-step explanation:

Part A:

we have three terms:

$3x^2y^2-2xy^2-8y^2$.

As all terms have $y^2$ we can factor the $y^2$

$3x^2y^2-2xy^2-8y^2= y^2(3x^2-2x-8)$.

Part B:

we have a trinomial

$x^2+10x+25$

As all terms are positive, we can factor it by searching two numbers that multiplied are 25 and added are 10, those are 5 and 5:

$x^2+10x+25= (x+5)(x+5) = (x+5)^2.$

Part C:

We have a binomial:

$x^2-36$

as both terms have square root, we can apply difference of perfect squares. That is, two factors with the roots, one with -6 and the other with 6:

$x^2-36=(x-6)(x+6).$

Answer 2

Hello,

1)
3x²y²-2xy²-8y²=y²(3x²-2x-8)
=y²(3x²-6x+4x-8)
=y²(3x(x-2)+4(x-2))
=y²(x-2)(3x+4)

2)
x²-36=x²-6²=(x+6)(x-6)