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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

If x+y=3 and x-y=5, then x^2-y^2=

(A) 4
(B) 8
(C) 15
(D) 16
(E) 64

答案和解析

答案：C

解析：

Recall that x^2-y^2 can be factored as (x+y)*(x-y). Since x+y = 3 and x-y = 5, their product, x^2-y^2, is (3)*(5), or 15.

Another method of solution is to solve the two equations x+y = 3 and x-y = 5 simultaneously to get x = 4 and y = -1. Then x^2-y^2 is 4^2-(-1)^2 = 16-1 = 15.