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Apply the distributive property to factor out the greatest common factor of all three terms.

24 c+36 d+18=

Apply the distributive property to factor out the greatest common factor of all three terms. $\newline$ $24 c+36 d+18=$

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Evaluate logarithms using properties

Full solution

Q. Apply the distributive property to factor out the greatest common factor of all three terms.

\newline

24 c+36 d+18=

Identify GCF of coefficients: Identify the greatest common factor (GCF) of the numerical coefficients $24$ , $36$ , and $18$ . $\newline$ To find the GCF, we list the factors of each number and find the largest factor that is common to all three. $\newline$ Factors of $24$ : $1$ , $2$ , $3$ , $4$ , $6$ , $8$ , $36$ $0$ , $24$ $\newline$ Factors of $36$ : $1$ , $2$ , $3$ , $4$ , $6$ , $36$ $8$ , $36$ $0$ , $18$ , $36$ $\newline$ Factors of $18$ : $1$ , $2$ , $3$ , $6$ , $36$ $8$ , $18$ $\newline$ The GCF is $6$ .
Use distributive property: Use the distributive property to factor out the GCF from each term. $\newline$ The distributive property states that $a(b + c) = ab + ac$ . $\newline$ Applying this to our expression, we get: $\newline$ $6\left(\frac{24c}{6} + \frac{36d}{6} + \frac{18}{6}\right)$ $\newline$ Perform the division for each term: $\newline$ $6(4c + 6d + 3)$
Perform division for each term: Check the factored expression to ensure that when the GCF is distributed back to each term, we get the original expression. $\newline$ $6 \times 4c = 24c$ $\newline$ $6 \times 6d = 36d$ $\newline$ $6 \times 3 = 18$ $\newline$ The original expression is recovered, so there is no math error.

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