Factor 64 f-64 g+96 to identify the equivalent expressions. Choose 2 answers: A 64(f-g+2) B 8(8f-8g+12) C 4(16 f-16+24 g) D 32(2f-2g+3)

Identify Common Factor: First, we look for a common factor in all three terms of the polynomial 64f - 64g + 96.Factor Out GCF: The common factor is 64 for the first two terms and 32 for the third term, but since we want a common factor for all terms, we take the greatest common factor, which is 32.Check Factored Expression: We factor out the 32 from each term: 32(2f - 2g + 3).Evaluate Option A: Now we check if the factored expression 32(2f - 2g + 3) is equivalent to any of the given options.Evaluate Option B: Option A is 64(f - g + 2), which is not equivalent to 32(2f - 2g + 3) because if we distribute 64, we get 64f - 64g + 128, which is not the original polynomial.Evaluate Option C: Option B is 8(8f - 8g + 12), which is equivalent to 32(2f - 2g + 3) because if we distribute 8, we get 64f - 64g + 96, which is the original polynomial.Option C is 4(16f - 16 + 24g), which is not equivalent to 32(2f - 2g + 3) because the terms inside the parentheses are not in the correct order, and there is a missing g in the second term.

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Factor
64 f-64 g+96 to identify the equivalent expressions.
Choose 2 answers:
A
64(f-g+2)
B
8(8f-8g+12)
C
4(16 f-16+24 g)
D
32(2f-2g+3)

Factor $64 f-64 g+96$ to identify the equivalent expressions. $\newline$ Choose $2$ answers: $\newline$ A $64(f-g+2)$ $\newline$ B $8(8 f-8 g+12)$ $\newline$ C $4(16 f-16+24 g)$ $\newline$ D $32(2 f-2 g+3)$

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Grade 7

Write variable expressions: word problems

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Q. Factor

64 f-64 g+96

to identify the equivalent expressions.

\newline

Choose

2

answers:

\newline

64(f-g+2)

\newline

8(8 f-8 g+12)

\newline

4(16 f-16+24 g)

\newline

32(2 f-2 g+3)

Identify Common Factor: First, we look for a common factor in all three terms of the polynomial $64f - 64g + 96$ .
Factor Out GCF: The common factor is $64$ for the first two terms and $32$ for the third term, but since we want a common factor for all terms, we take the greatest common factor, which is $32$ .
Check Factored Expression: We factor out the $32$ from each term: $32(2f - 2g + 3)$ .
Evaluate Option A: Now we check if the factored expression $32(2f - 2g + 3)$ is equivalent to any of the given options.
Evaluate Option B: Option A is $64(f - g + 2)$ , which is not equivalent to $32(2f - 2g + 3)$ because if we distribute $64$ , we get $64f - 64g + 128$ , which is not the original polynomial.
Evaluate Option C: Option B is $8(8f - 8g + 12)$ , which is equivalent to $32(2f - 2g + 3)$ because if we distribute $8$ , we get $64f - 64g + 96$ , which is the original polynomial.
Evaluate Option C: Option B is $8(8f - 8g + 12)$ , which is equivalent to $32(2f - 2g + 3)$ because if we distribute $8$ , we get $64f - 64g + 96$ , which is the original polynomial.Option C is $4(16f - 16 + 24g)$ , which is not equivalent to $32(2f - 2g + 3)$ because the terms inside the parentheses are not in the correct order, and there is a missing $g$ in the second term.