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 - 16x², the difference of squares

Explanation:

Step1: Recall the difference of squares formula

The difference of squares formula is $(a - b)(a + b) = a^2 - b^2$.

Step2: Identify \(a\) and \(b\) in the given expression

In the expression \((9y^{2}-4x)(9y^{2}+4x)\), we have \(a = 9y^{2}\) and \(b = 4x\).

Step3: Apply the difference of squares formula

Using the formula \((a - b)(a + b)=a^{2}-b^{2}\), we substitute \(a = 9y^{2}\) and \(b = 4x\):

$$
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Since the expression is in the form of \((a - b)(a + b)\), it is the difference of squares.

Answer:

B. \(81y^{4}-16x^{2}\), the difference of squares