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Problem 360

# Factor $$a x+b y+a y+b x$$ completely

Expert verified
The given expression can be factored completely as $$(a+b)(x+y)$$.
See the step by step solution

## 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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