2006 AMC 12B Problems/Problem 2

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Problem

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

$\text {(A) } - 72 \qquad \text {(B) } - 27 \qquad \text {(C) } - 24 \qquad \text {(D) } 24 \qquad \text {(E) } 72$

Solution

$4\spadesuit 5=-9$

$3\spadesuit -9=-72 \Rightarrow \text{(B)}$

See also

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