PSAT Math Multiple-Choice Question 474: Answer and Explanation

Question: 474

Which of the following is equivalent to 64x² - 81y²?

• A. (8x + 9y)(8x - 9y)
• B. (9x + 8y)(9x - 8y)
• C. (8x + 9y)²
• D. (8x - 9y)²

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Classic Quadratics

Getting to the Answer: Notice that this quadratic is a difference of squares, so use the formula a² - b² = (a + b)(a - b). Set a² equal to 64x² and take the square root of both sides to find that a = 8x. Do the same thing with b² and 81y² to find that b = 9y. Fill in (a + b)(a - b) with the values you found for a and b to get (8x + 9y)(8x - 9y). Therefore, (A) is correct.