Factor 18 p-36 to identify the equivalent expressions. Choose 2 answers: A 3(9p-12) B 9(2p-4p) c 2(9p-18) D 18(p-2)

Identify GCF: First, we need to identify the greatest common factor (GCF) of the terms 18p and 36. The GCF of 18p and 36 is 18 since 18 is the largest number that divides both terms without a remainder.Factor Out GCF: Now, we factor out the GCF from each term. This gives us: 18p - 36 = 18(p) - 18(2)Simplify Expression: Simplify the expression inside the parentheses to get the factored form: 18(p) - 18(2) = 18(p - 2)Check Options: Now, let's check the given options to see which ones are equivalent to the factored expression 18(p - 2). Option A: 3(9p - 12) = 27p - 36, which is not equivalent to 18(p - 2) because 27p is not the same as 18p. Option B: 9(2p - 4p) = 9(-2p), which is not equivalent to 18(p - 2) because the sign and coefficients do not match. Option C: 2(9p - 18) = 18p - 36, which is equivalent to 18(p - 2) because when we distribute the 2, we get the original expression. Option D: 18(p - 2) is the same as the factored expression we found, so it is equivalent. Therefore, the correct options are C and D.

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Factor
18 p-36 to identify the equivalent expressions.
Choose 2 answers:
A
3(9p-12)
B
9(2p-4p)
c
2(9p-18)
D
18(p-2)

Factor $18 p-36$ to identify the equivalent expressions. $\newline$ Choose $2$ answers: $\newline$ A $3(9 p-12)$ $\newline$ B $9(2 p-4 p)$ $\newline$ c $2(9 p-18)$ $\newline$ D $18(p-2)$

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Math Problems

Grade 6

Factor numerical expressions using the distributive property

Full solution

Q. Factor

18 p-36

to identify the equivalent expressions.

\newline

Choose

2

answers:

\newline

3(9 p-12)

\newline

9(2 p-4 p)

\newline

2(9 p-18)

\newline

18(p-2)

Identify GCF: First, we need to identify the greatest common factor (GCF) of the terms $18p$ and $36$ . The GCF of $18p$ and $36$ is $18$ since $18$ is the largest number that divides both terms without a remainder.
Factor Out GCF: Now, we factor out the GCF from each term. This gives us: $\newline$ $18p - 36 = 18(p) - 18(2)$
Simplify Expression: Simplify the expression inside the parentheses to get the factored form: $18(p) - 18(2) = 18(p - 2)$
Check Options: Now, let's check the given options to see which ones are equivalent to the factored expression $18(p - 2)$ . $\newline$ Option A: $3(9p - 12) = 27p - 36$ , which is not equivalent to $18(p - 2)$ because $27p$ is not the same as $18p$ . $\newline$ Option B: $9(2p - 4p) = 9(-2p)$ , which is not equivalent to $18(p - 2)$ because the sign and coefficients do not match. $\newline$ Option C: $2(9p - 18) = 18p - 36$ , which is equivalent to $18(p - 2)$ because when we distribute the $2$ , we get the original expression. $\newline$ Option D: $18(p - 2)$ is the same as the factored expression we found, so it is equivalent. $\newline$ Therefore, the correct options are C and D.