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algebra senior

Problem

Simplify

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

(A)

a^{2} x^{2} + b^{2} y^{2}

(B)

(a x + b y)^{2}

(C)

(a x + b y) (b x + a y)

(D)

2 (a^{2} x^{2} + b^{2} y^{2})

Solution

We can multiply each answer choice by

b x + a y

and then compare with the numerator. This gives

(a x + b y)^{2}

.

Final answer

B