1988 AHSME Problems/Problem 19

Revision as of 13:05, 27 February 2018 by Hapaxoromenon (talk | contribs) (Added a solution with explanation)

Problem

Simplify

$\frac{bx(a^2x^2 + 2a^2y^2 + b^2y^2) + ay(a^2x^2 + 2b^2x^2 + b^2y^2)}{bx + ay}$

$\textbf{(A)}\ a^2x^2 + b^2y^2\qquad \textbf{(B)}\ (ax + by)^2\qquad \textbf{(C)}\ (ax + by)(bx + ay)\qquad\\ \textbf{(D)}\ 2(a^2x^2+b^2y^2)\qquad \textbf{(E)}\ (bx+ay)^2$


Solution

The fastest way is to multiply each answer choice by $bx + ay$ and then compare to the numerator. This gives $\boxed{\text{B}}$.


See also

1988 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 18
Followed by
Problem 20
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