Full solution

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

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24+28=

Identify GCF of $24$ and $28$ : Identify the greatest common factor (GCF) of $24$ and $28$ . $\newline$ To find the GCF, list the factors of each number and find the largest factor they have in common. $\newline$ Factors of $24$ : $1$ , $2$ , $3$ , $4$ , $6$ , $28$ $0$ , $28$ $1$ , $24$ $\newline$ Factors of $28$ : $1$ , $2$ , $4$ , $28$ $7$ , $28$ $8$ , $28$ $\newline$ The GCF of $24$ and $28$ is $4$ .
Factor out GCF using distributive property: Use the distributive property to factor out the GCF from the expression $24 + 28$ . $\newline$ The distributive property states that $a(b + c) = ab + ac$ . $\newline$ Here, we can factor out the GCF, which is $4$ , from both terms. $\newline$ So, $24 + 28$ can be written as $4(6) + 4(7)$ .
Combine factored terms: Combine the factored terms. $\newline$ Using the distributive property, we combine the terms to get: $\newline$ $4(6 + 7)$
Simplify expression inside parentheses: Simplify the expression inside the parentheses. $\newline$ $6 + 7 = 13$ . $\newline$ So, $4(6 + 7)$ becomes $4(13)$ .
Multiply GCF by simplified expression: Multiply the GCF by the simplified expression. $\newline$ $4 \times 13 = 52$ . $\newline$ So, the final factored expression is $4(13)$ .