Question

Which is equivalent to (9 y squared minus 4 x)(9 y squared + 4 x), and what type of special product is it?

81 y Superscript 4 Baseline minus 16 x squared, a perfect square trinomial
81 y Superscript 4 Baseline minus 16 x squared, the difference of squares
81 y Superscript 4 Baseline minus 72 x y squared minus 16 x squared, a perfect square trinomial
81 y Superscript 4 Baseline minus 72 x y squared minus 16 x squared, the difference of squares

Answer 1

(9y^2 − 4x)(9y^2 + 4x) = (a − b)(a + b) with a = 9y^2, b = 4x, so = a^2 − b^2 = (9y^2)^2 − (4x)^2 = 81y^4 − 16x^2.

This is the difference of squares.