Questions: Factor by grouping. x^2 + 7xy + 3x + 21y =

Factor by grouping. x^2 + 7xy + 3x + 21y =
Transcript text: Factor by grouping. \[ x^{2}+7 x y+3 x+21 y= \]
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Solution

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Solution Steps

To factor by grouping, we need to group the terms in pairs and factor out the common factors from each pair. Then, we look for a common binomial factor in the resulting expression.

Step 1: Group the Terms

Group the terms in pairs: \[ x^2 + 7xy + 3x + 21y = (x^2 + 7xy) + (3x + 21y) \]

Step 2: Factor Out the Common Factors

Factor out the common factors from each pair: \[ (x^2 + 7xy) + (3x + 21y) = x(x + 7y) + 3(x + 7y) \]

Step 3: Factor Out the Common Binomial

Factor out the common binomial \((x + 7y)\): \[ x(x + 7y) + 3(x + 7y) = (x + 3)(x + 7y) \]

Final Answer

\[ \boxed{(x + 3)(x + 7y)} \]

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