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Chapter 15: Chapter 15

Problem 360

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Factor \(a x+b y+a y+b x\) completely

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The given expression can be factored completely as \((a+b)(x+y)\).
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Identify Common Factors

Observe that there are two common factors in the given expression: \(ax + bx\) and \(ay + by\). We can rewrite the expression by grouping these terms together: \[(a+b)x + (a+b)y.\]

Step 2: Factor by Distributive Property

Since both terms have a common factor of \((a+b)\), we can use the distributive property to factor out the common term: \[(a+b)(x+y).\] Thus, the given expression is factored completely as \((a+b)(x+y)\).

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