Question

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

Part B: Factor x2 + 10x + 25. Show your work. (3 points)

Part C: Factor x2 − 36. Show your work. (3 points)
Please help!!!!!!!!!!!!!

Answer 1

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)

Answer 2

Check below.

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).`