Completely factor the expression 2a3 − 128. A. 2(a − 4)3

B. 2(a − 4)(a2 + 4a + 16)
C. 2(a3 − 64)
D. Prime

Completely factor the expression 7(x − y) − z(x − y). A. Prime
B. (x − y)(7 − z)
C. (x − y)(7 + z)
D. (x − y)2(7 − z)3

Find the product of –3a3b(2a0b4 − 4a2b3) A. –6b5 + 14a5b4
B. –6b4 + 12a6b3
C. 14a5b4 − 6b5
D. 12a5b4 − 6a3b5

Completely factor the expression r2 − 2r + 1. A. (r + 1)(r − 1)
B. (r − 1)(r − 1)
C. r(r − 2) + 1
D. Prime

Simplify the expression 2ab4 − 3a2b2 − ab4 + a2b2. A. a2b8 − a2b8 − 2a4b4
B. 0
C. 2a2b8 − 3a4b4 D. ab4 − 2a2b2

Completely factor the expression a2 + 4b − ab − 4a. A. (a + b)(a − 4)
B. Prime
C. (a − b)(a − 4)
D. (a + b)(a + 4)

plb help me i am geting confuse

and this please

Find the product of (x − 2y)2. A. x2 + 4xy + 4y2
B. x2 + 2xy + 4y2
C. x2 − 4xy + 4y2
D. x2 + 4y2

To completely factor an expression, we need to find the common factors and then use factoring techniques such as factoring by grouping, difference of squares, or perfect square trinomials. Let's go through each expression and find the correct factorization.

1. Completely factor the expression 2a^3 − 128. The common factor here is 2, so we can factor it out:
2(a^3 − 64). Now we recognize that (a^3 − 64) is a difference of cubes, which factors as (a − 4)(a^2 + 4a + 16). Therefore, the complete factorization is 2(a − 4)(a^2 + 4a + 16). The correct answer is B.

2. Completely factor the expression 7(x − y) − z(x − y). Here we have a common factor of (x − y), which we can factor out:
(x − y)(7 − z). The correct answer is B.

3. Find the product of –3a^3b(2a^0b^4 − 4a^2b^3). First, simplify 2a^0 to 2. Now we can multiply the terms:
–3a^3b(2b^4 − 4a^2b^3) = –6a^3b^5 + 12a^5b^4. The correct answer is D.

4. Completely factor the expression r^2 − 2r + 1. This expression is a perfect square trinomial because the first and last terms are perfect squares. It factors as (r − 1)(r − 1), which simplifies to (r − 1)^2. The correct answer is B.

5. Simplify the expression 2ab^4 − 3a^2b^2 − ab^4 + a^2b^2. Here we can combine like terms:
2ab^4 − ab^4 − 3a^2b^2 + a^2b^2 = ab^4 − 2a^2b^2. The correct answer is D.

6. Completely factor the expression a^2 + 4b − ab − 4a. This expression does not have any common factors, so it cannot be completely factored. The correct answer is B, Prime.

Remember, when factoring an expression, it's important to look for any common factors and then apply appropriate factoring techniques such as factoring out common terms or recognizing specific patterns.