Factor $64 b-16 c$ to identify the equivalent expressions. $\newline$ Choose $2$ answers: $\newline$ A $16(4 b-c)$ $\newline$ B $4(16 b-4)$ $\newline$ c $8(8 b+2 c)$ $\newline$ D $2(32 b-8 c)$

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Math Problems

Grade 6

Factor numerical expressions using the distributive property

Full solution

Q. Factor

64 b-16 c

to identify the equivalent expressions.

\newline

Choose

2

answers:

\newline

16(4 b-c)

\newline

4(16 b-4)

\newline

8(8 b+2 c)

\newline

2(32 b-8 c)

Identify GCF: Step Title: Identify the Greatest Common Factor (GCF) $\newline$ Concise Step Description: Determine the greatest common factor that can be factored out from both terms in the expression $64b - 16c$ . $\newline$ Step Calculation: The GCF of $64$ and $16$ is $16$ . $\newline$ Step Output: GCF: $16$
Factor Out GCF: Step Title: Factor Out the GCF $\newline$ Concise Step Description: Factor out the GCF from the expression to simplify it. $\newline$ Step Calculation: Factoring out $16$ from $64b - 16c$ gives us $16(4b - c)$ . $\newline$ Step Output: Factored Expression: $16(4b - c)$
Verify Factored Expression: Step Title: Verify the Factored Expression $\newline$ Concise Step Description: Check if the factored expression is equivalent to the original expression by distributing the GCF back into the factored terms. $\newline$ Step Calculation: Distributing $16$ into $(4b - c)$ gives us $16\times 4b - 16\times c$ , which simplifies to $64b - 16c$ . $\newline$ Step Output: Verified Expression: $64b - 16c$
Compare with Choices: Step Title: Compare with the Answer Choices $\newline$ Concise Step Description: Compare the factored expression with the given answer choices to identify the equivalent expressions. $\newline$ Step Calculation: The factored expression $16(4b - c)$ matches with choice A. Now, let's check if any other choices are equivalent. $\newline$ Step Output: Matching Choice: A
Check Other Choices: Step Title: Check Other Answer Choices $\newline$ Concise Step Description: Check if any other answer choices are equivalent to the factored expression by simplifying them. $\newline$ Step Calculation: Choice B simplifies to $4\times16b - 4\times4$ which is $64b - 16c$ , so choice B is also equivalent. Choices C and D do not simplify to the original expression. $\newline$ Step Output: Equivalent Choices: A and B