Question

Factor the expression completely: 16x - 625y.

a) (4x + 25y)(4x - 25y)
b) (4x + 25y)²
c) 4(4x - 25y)
d) (16x - 25y)(16x + 25y)

Answer 1

The expression 16x - 625y is factored as the difference of squares and the correct factored form is (4x + 25y)(4x - 25y), which is option a).

Step-by-step explanation:

The expression 16x - 625y can be factored by recognizing it as a difference of squares, which is a binomial of the form a² - b² that can be factored into (a + b)(a - b). In this case, 16x is a perfect square, being the square of 4x, and 625y is the square of 25y. Thus, the factored form of the expression is (4x + 25y)(4x - 25y), which corresponds to option a).