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2008 AMC 12B Problems/Problem 7

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Problem 7

For real numbers $a$ and $b$ , define $a\$ $b = (a - b)^2$ . What is $(x - y)^2\$ $(y - x)^2$ ?

$\textbf{(A)}\ 0 \qquad \textbf{(B)}\ x^2 + y^2 \qquad \textbf{(C)}\ 2x^2 \qquad \textbf{(D)}\ 2y^2 \qquad \textbf{(E)}\ 4xy$

Solution

$\left[ (x-y)^2 - (y-x)^2 \right]^2$

$\left[ (x-y)^2 - (x-y)^2 \right]^2$

$0 \Rightarrow \textbf{(A)}$

See Also

2008 AMC 12B (Problems • Resources)
Preceded by Problem 6	Followed by Problem 8
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25

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Want to learn how to tackle those tough MATHCOUNTS and AMC counting and probability problems? Check out Art of Problem Solving's Introduction to Counting & Probability by David Patrick.

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