Question

Which is equivalent to (9y2 – 4x)(9y2 + 4x), and what type of special product is it?

81y4 – 16x2, a perfect square trinomial
81y4 – 16x2, the difference of squares
81y4 – 72xy2 – 16x2, a perfect square trinomial
81y4 – 72xy2 – 16x216, the difference of squares

Answer 1

Consider the expression
`(9y^2- 4x)(9y^2 + 4x) .` You can see that in both brackets are the same terms
`9y^2` and
`4x`, but signs are different. So you can use formula for the difference of squares:

`a^2-b^2=(a-b)(a+b).`

According to this formula,

`(9y^2-4x)(9y^2+4x)=(9y^2)^2-(4x)^2=9^2\cdot (y^2)^2-4^2\cdot x^2=81y^4-16x^2.`

Answer: correct choice is B.