Question

Factor 16x^4 - 49y^2 for u and v.

a) 4x^2 - 7y
b) (4x^2 - 7y)(4x^2 + 7y)
c) (4x^2 - 7y)(4x^2 - 7y)
d) 16x^4 - 49y^2

Answer 1

The expression 16x^4 - 49y^2 is a difference of squares and can be factored as (4x^2 - 7y)(4x^2 + 7y), which corresponds to option (b).

Step-by-step explanation:

To factor the expression 16x^4 - 49y^2, we recognize that this is a difference of squares, which can be factored into the product of the sum and difference of the square roots of each term. The square root of 16x^4 is 4x^2, and the square root of 49y^2 is 7y. Applying the difference of squares formula a^2 - b^2 = (a - b)(a + b), we get the factored form:

(4x^2 - 7y)(4x^2 + 7y)

The correct answer to the question of how to factor 16x^4 - 49y^2 is choice (b) (4x^2 - 7y)(4x^2 + 7y).