2008 AMC 10B Problems/Problem 5: Difference between revisions

Revision as of 15:22, 10 October 2008

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

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

Since $(-a)^2 = a^2$ , it follows that $(x-y)^2 = (y-x)^2$ , and

$(x-y)^2\$ $(y-x)^2 = [(x-y)^2 - (y-x)^2]^2 = [(x-y)^2 - (x-y)^2]^2 = 0\ \mathrm{(A)}.$

2008 AMC 10B (Problems • Answer Key • Resources)
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All AMC 10 Problems and Solutions

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 ==Problem==
-For [[real number]]s <math>a</math> and <math>b</math>, define <math>a\</math><math> b=(a-b)^2</math>. What is <math>(x-y)^2\</math><math> (y-x)^2</math>?
+For [[real number]]s <math>a</math> and <math>b</math>, define <math>a * b=(a-b)^2</math>. What is <math>(x-y)^2 * (y-x)^2</math>?
 <math>\mathrm{(A)}\ 0\qquad\mathrm{(B)}\ x^2+y^2\qquad\mathrm{(C)}\ 2x^2\qquad\mathrm{(D)}\ 2y^2\qquad\mathrm{(E)}\ 4xy</math>