PLZ HELP ASAP! I WILL MARK BRAINIEST An expression is shown below: 2x^3y + 8xy − 4x^2y − 16y
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)

Step-by-step explanation:

If we look, "y" can be factored out of the entire expression because it goes into them all. This gives y(2x^3 - 4x^2 + 8x - 16)

Since everything inside the brackets is a multiple of 2 we can factor it out.

2y (x^3 - 2x^2 + 8x - 16)

Here to factor (x^3 - 2x^2 + 8x - 16) we could either use a calculator, or notice that when we subsitute 2 into the equation, it equals 0. Therefore (x - 2) must be a factor. The other factor must be (x^2 + 8) because:

(x - 2) (      )

We need to have 1 x^3 so we know the first part of the factor must be x^2

The also need to have -16 when we multiply this out, -2 * something equals -16. Meaning we must have 8 inside of the brackets.

This gives :

(x - 2) (x^2 + 8).

When we expand this out we get (x^3 - 2x^2 + 8x - 16)

Therefore in total we have

2y (x - 2)(x^2 + 8)

There are other methods of factorising (x^3 - 2x^2 + 8x - 16), so use the method which you have been taught in class or the one I used.

we need the options

step-by-step explanation: