Factor 48 m+42 n to identify the equivalent expressions. Choose 2 answers: A 6(8m+7n) B 3(16 m+14 n) c 2(12 m+21 n) D 7(7m+6n)

Identify GCF: Identify the greatest common factor (GCF) of the coefficients 48 and 42. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. The greatest common factor is 6.Find Factors: Divide both terms of the expression 48m + 42n by the GCF, which is 6. 48m ÷ 6 = 8m 42n ÷ 6 = 7n So, 48m + 42n factored by 6 is 6(8m + 7n).Divide by GCF: Check the answer choices to see which ones match the factored expression 6(8m + 7n). Choice A is 6(8m+7n), which matches our factored expression. Choice B is 3(16m+14n), which does not match because 16m+14n is not the result of dividing 48m+42n by 3. Choice C is 2(12m+21n), which does not match because 12m+21n is not the result of dividing 48m+42n by 2. Choice D is 7(7m+6n), which does not match because 7m+6n is not the result of dividing 48m+42n by 7.

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Factor
48 m+42 n to identify the equivalent expressions.
Choose 2 answers:
A
6(8m+7n)
B
3(16 m+14 n)
c
2(12 m+21 n)
D
7(7m+6n)

Factor $48 m+42 n$ to identify the equivalent expressions. $\newline$ Choose $2$ answers: $\newline$ A $6(8 m+7 n)$ $\newline$ B $3(16 m+14 n)$ $\newline$ C $2(12 m+21 n)$ $\newline$ D $7(7 m+6 n)$

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Math Problems

Grade 7

Identify equivalent linear expressions I

Full solution

Q. Factor

48 m+42 n

to identify the equivalent expressions.

\newline

Choose

2

answers:

\newline

6(8 m+7 n)

\newline

3(16 m+14 n)

\newline

2(12 m+21 n)

\newline

7(7 m+6 n)

Identify GCF: Identify the greatest common factor (GCF) of the coefficients $48$ and $42$ . The factors of $48$ are $1, 2, 3, 4, 6, 8, 12, 16, 24, 48$ . The factors of $42$ are $1, 2, 3, 6, 7, 14, 21, 42$ . The greatest common factor is $6$ .
Find Factors: Divide both terms of the expression $48m + 42n$ by the GCF, which is $6$ . $\newline$ $48m \div 6 = 8m$ $\newline$ $42n \div 6 = 7n$ $\newline$ So, $48m + 42n$ factored by $6$ is $6(8m + 7n)$ .
Divide by GCF: Check the answer choices to see which ones match the factored expression $6(8m + 7n)$ . $\newline$ Choice A is $6(8m+7n)$ , which matches our factored expression. $\newline$ Choice B is $3(16m+14n)$ , which does not match because $16m+14n$ is not the result of dividing $48m+42n$ by $3$ . $\newline$ Choice C is $2(12m+21n)$ , which does not match because $12m+21n$ is not the result of dividing $48m+42n$ by $2$ . $\newline$ Choice D is $6(8m+7n)$ $0$ , which does not match because $6(8m+7n)$ $1$ is not the result of dividing $48m+42n$ by $6(8m+7n)$ $3$ .