PSAT Math Grid-Ins Question 31: Answer and Explanation

Question: 31

(gx² - 4y²)(6x² + hy²)

In the expression above, g and h are non-zero constants with a difference of 5. If the value of the coefficient on the x²y² term is zero when the expression is multiplied out and the like terms are collected, what is the value of gh?

Correct Answer: 24

Explanation:

24

The question asks about the product of two coefficients within a pair of binomials. When given a quadratic in factored form, it is often necessary to use FOIL to multiply the factors out to the standard form ax² + bx + c to solve the question. The expression becomes 6gx⁴ + ghx²y² - 3Ax²y¹ - 4hy⁴. It might be tempting to try to figure out what the values of g and h are, given the information that they have a difference of 5. However, make sure to read the full question, which asks for the value of gh, not g or h separately. The gh appears as the coefficient of one of the x²y² terms, and the question states that the coefficient on that term when like terms are collected is zero. The second x²y² term has a coefficient of -24, so the first one must have a coefficient of 24 in order to equal 0 when the two terms are combined. Thus, gh must equal 24. The correct answer is 24.