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2006 AMC 10B Problem 2

Problem 2 of 25EasierAlgebra

For real numbers xx and y,y, define x♠y=(x+y)(x−y).x \spadesuit y = (x+y)(x-y). What is 3♠(4♠5)?3 \spadesuit (4 \spadesuit 5)?

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Solution

Since x♠y=(x+y)(x−y)=x2−y2,x \spadesuit y = (x+y)(x-y) = x^2 - y^2, we have 4♠5=16−25=−9.4 \spadesuit 5 = 16 - 25 = -9. Then 3♠(−9)=9−81=−72.3 \spadesuit (-9) = 9 - 81 = -72. Thus, the correct answer is A.
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Tagged: custom operation · difference of squares

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