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Algebra Difficulty 1.7 Junior Find the answer

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

Pick one

Solution

Since x♠y=(x+y)(x−y)x \spadesuit y = (x+y)(x-y):
3♠(4♠5)=3♠((4+5)(4−5))=3♠(−9)=(3+(−9))(3−(−9))=(A)−723 \spadesuit (4 \spadesuit 5) = 3 \spadesuit((4+5)(4-5)) = 3 \spadesuit (-9) = (3+(-9))(3-(-9)) = \boxed{\textbf{(A)}-72}

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.