Which of the following is equivalent to 18 more than the product of 9-6p and p-2 ? Choose 1 answer: (A) 3(7p+6) (B) -3p(2p-7) (c) (27-6p)(p-2) (D) (9-6p)(p+16)

Understand the problem: Understand the problem. We need to find an expression that is equivalent to 18 more than the product of (9-6p) and (p-2).Calculate the product: Calculate the product of (9-6p) and (p-2). (9-6p)(p-2) = 9(p-2) - 6p(p-2) = 9p - 18 - 6p^2 + 12p = -6p^2 + 21p - 18Add 18 to the product: Add 18 to the product to get the equivalent expression. -6p^2 + 21p - 18 + 18 = -6p^2 + 21pCheck the answer choices: Check the answer choices to see which one matches the equivalent expression. (A) 3(7p+6) = 21p + 18 (This does not match because of the extra +18) (B) -3p(2p-7) = -6p^2 + 21p (This matches our equivalent expression) (C) (27-6p)(p-2) (This expands to a different expression) (D) (9-6p)(p+16) (This expands to a different expression)Choose the correct answer: Choose the correct answer based on the matching expression. The correct answer is (B) -3p(2p-7).

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Which of the following is equivalent to 18 more than the product of
9-6p and
p-2 ?
Choose 1 answer:
(A)
3(7p+6)
(B)
-3p(2p-7)
(c)
(27-6p)(p-2)
(D)
(9-6p)(p+16)

Which of the following is equivalent to $18$ more than the product of $9-6 p$ and $p-2$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $3(7 p+6)$ $\newline$ (B) $-3 p(2 p-7)$ $\newline$ (C) $(27-6 p)(p-2)$ $\newline$ (D) $(9-6 p)(p+16)$

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Math Problems

Grade 7

Identify equivalent linear expressions I

Full solution

Q. Which of the following is equivalent to

18

more than the product of

9-6 p

and

p-2

\newline

Choose

1

answer:

\newline

(A)

3(7 p+6)

\newline

(B)

-3 p(2 p-7)

\newline

(C)

(27-6 p)(p-2)

\newline

(D)

(9-6 p)(p+16)

Understand the problem: Understand the problem. $\newline$ We need to find an expression that is equivalent to $18$ more than the product of $(9-6p)$ and $(p-2)$ .
Calculate the product: Calculate the product of $(9-6p)$ and $(p-2)$ . $(9-6p)(p-2) = 9(p-2) - 6p(p-2)$ $= 9p - 18 - 6p^2 + 12p$ $= -6p^2 + 21p - 18$
Add $18$ to the product: Add $18$ to the product to get the equivalent expression. $\newline$ $-6p^2 + 21p - 18 + 18 = -6p^2 + 21p$
Check the answer choices: Check the answer choices to see which one matches the equivalent expression. $\newline$ (A) $3(7p+6) = 21p + 18$ (This does not match because of the extra $+18$ ) $\newline$ (B) $-3p(2p-7) = -6p^2 + 21p$ (This matches our equivalent expression) $\newline$ (C) $(27-6p)(p-2)$ (This expands to a different expression) $\newline$ (D) $(9-6p)(p+16)$ (This expands to a different expression)
Choose the correct answer: Choose the correct answer based on the matching expression. $\newline$ The correct answer is $(B) -3p(2p-7)$ .