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Quiz 3
Apply the distributive property to factor out the greatest common factor.

22 c+33 d=1
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Apply the distributive property to factor out the greatest common factor. $\newline$ 22c+33d=_______

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Evaluate two-variable equations: word problems

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Q. Apply the distributive property to factor out the greatest common factor.

\newline

22c+33d=_______

Identify GCF of coefficients: Identify the greatest common factor (GCF) of the coefficients $22$ and $33$ . To find the GCF of $22$ and $33$ , we list the factors of each number: Factors of $22$ : $1$ , $2$ , $11$ , $22$ Factors of $33$ : $1$ , $33$ $1$ , $11$ , $33$ The greatest common factor of $22$ and $33$ is $11$ .
Use distributive property: Use the distributive property to factor out the GCF from the expression $22c + 33d$ . We can write the expression as a product of the GCF and the remaining terms: $22c + 33d = 11(2c) + 11(3d)$ Now, we factor out the $11$ : $22c + 33d = 11(2c + 3d)$
Check factored expression: Check the factored expression to ensure that when the distributive property is applied, we get the original expression. $\newline$ $11(2c + 3d) = 11\times 2c + 11\times 3d$ $\newline$ $= 22c + 33d$ $\newline$ The factored expression is correct and matches the original expression.

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