# SAT Math Multiple Choice Question 164: Answer and Explanation

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**Question: 164**

**14.** If r = (a + b)^{2} and s = -4ab + 3b, what is r - 2s in terms of a and b ?

- A. a
^{2}+ b^{2}- 7ab - 6b - B. a
^{2}+ b^{2}- 7ab + 6b - C. a
^{2}+ b^{2}+ 9ab - 6b - D. a
^{2}+ b^{2}+ 9ab - 6b

**Correct Answer:** C

**Explanation:**

C Whenever there are variables in the question and in the answers, think Plugging In. If a = 2 and b = 3, r = [ (2) + 3]^{2} = (1 + 3)^{2} = 16, and s = -4(2)(3) + 3(3) = -24 + 9 = -15. The expression r - 2s becomes 16 - 2(-15) = 16 + 30 = 46. Plug 2 in for a and 3 in for b in each of the answers to see which answer equals the target number of 46. Choice (A) becomes (2^{2}) + 3^{2} - 7(2)(3) - 6(3) = 1 + 9 - 42 - 18 = -50. This does not match the target number, so eliminate (A). Choice (B) becomes (2^{2}) + 3^{2} - 7(2)(3) + 6(3) = 1 + 9 - 42 + 18 = -14. Eliminate (B). Choice (C) becomes (2^{2}) + 3^{2} + 9(2)(3) - 6(3) = 1 + 9 + 54 - 18 = 46. Keep (C), but check (D) just in case it also works. Choice (D) is the same as (C) except for the coefficient on the a^{2} term, so it can't equal 46. Eliminate (D). The correct answer is (C).