Questions: Factor out the greatest common factor. 2t(u+5v)+9(u+5v)=

Factor out the greatest common factor. 2t(u+5v)+9(u+5v)=
Transcript text: Factor out the greatest common factor. \[ 2 t(u+5 v)+9(u+5 v)= \]
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Solution

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Solution Steps

To factor out the greatest common factor (GCF) from the given expression, we first identify the common factor in both terms. Here, the common factor is \((u + 5v)\). We then factor out \((u + 5v)\) from the expression.

Step 1: Identify the Common Factor

We start with the expression: \[ 2t(u + 5v) + 9(u + 5v) \] We observe that \((u + 5v)\) is a common factor in both terms.

Step 2: Factor Out the Common Factor

We factor out \((u + 5v)\) from the expression: \[ 2t(u + 5v) + 9(u + 5v) = (2t + 9)(u + 5v) \]

Final Answer

\[ \boxed{(2t + 9)(u + 5v)} \]

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