Question

Factor the expression (2 + 4)^2 - 4y(x + 4) + 4y10.

a. (2y - 4)(x + 2y + 20)
b. (2x - 4y)(x - 2y + 20)
c. (2 + 4y)(x - 2y - 20)
d. (x + 2y)(x - 4y + 20)

Answer 1

The expression can be factored as (2 + 4y)(x - 2y - 6).

Step-by-step explanation:

To factor the expression (2 + 4)^2 - 4y(x + 4) + 4y10, we can start by expanding the squared term: (2 + 4)^2 = 6^2 = 36.

Next, we can distribute the -4y to the terms inside the parentheses: -4y(x + 4) = -4yx - 16y.

Combining all the terms, we have: 36 - 4yx - 16y + 4y10.

Simplifying further, we get the expression -4yx - 16y + 40y - 4yx + 36.

Grouping like terms, we have -8yx + 24y + 36.

Factoring out common factors, we get -8yx + 12(2y + 3).

So, the correct factorization is (2 + 4y)(x - 2y - 6).