Question

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

Answer 1

The product of (9y²-4x)(9y²+4x) is equivalent to 81y´ - 16x², representing the difference of squares, which is a special product in algebra.

Step-by-step explanation:

The product of (9y²-4x)(9y²+4x) is equivalent to (9y²)² - (4x)². This is known as the difference of squares since it follows the formula (a² - b²), where a = 9y² and b = 4x. The expression simplifies to 81y´ - 16x².

To arrive at this answer, we apply the formula for the difference of squares, which states that the product of two binomials in the form (a+b)(a-b) equals a² - b². Here's the step-by-step process:

1. Identify a as 9y² and b as 4x.
2. Square a: (9y²)² = 81y´.
3. Square b: (4x)² = 16x².
4. Subtract the square of b from the square of a: 81y´ - 16x².