Which of the following is equivalent to -8x^(2)-8xy+12y^(2) ? Choose 1 answer: (A) -4(2x^(2)-2xy-3y^(2)) (B) -4(2x^(2)-2xy+3y^(2)) (C) -4(2x^(2)+2xy-3y^(2)) (D) -4(2x^(2)+2xy+3y^(2))

Factor Out GCF: We need to factor out the greatest common factor from the expression -8x^(2)-8xy+12y^(2). The greatest common factor is -4. Factor out -4 from each term in the expression.Rewrite Expression: After factoring out -4, we rewrite the expression as: -4(2x^(2) + 2xy - 3y^(2)). However, we need to be careful with the signs. The original expression has a negative sign in front of the xy term, so we should have: -4(2x^(2) - 2xy + 3y^(2)).Check Answer Choices: Now, let's check each answer choice to see which one matches our factored expression: (A) -4(2x^(2)-2xy-3y^(2)) does not match because the sign in front of 3y^(2) is negative. (B) -4(2x^(2)-2xy+3y^(2)) matches our factored expression. (C) -4(2x^(2)+2xy-3y^(2)) does not match because the sign in front of 2xy is positive. (D) -4(2x^(2)+2xy+3y^(2)) does not match because both signs in front of 2xy and 3y^(2) are positive.

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Which of the following is equivalent to
-8x^(2)-8xy+12y^(2) ?
Choose 1 answer:
(A)
-4(2x^(2)-2xy-3y^(2))
(B)
-4(2x^(2)-2xy+3y^(2))
(C)
-4(2x^(2)+2xy-3y^(2))
(D)
-4(2x^(2)+2xy+3y^(2))

Which of the following is equivalent to $-8 x^{2}-8 x y+12 y^{2}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-4\left(2 x^{2}-2 x y-3 y^{2}\right)$ $\newline$ (B) $-4\left(2 x^{2}-2 x y+3 y^{2}\right)$ $\newline$ (C) $-4\left(2 x^{2}+2 x y-3 y^{2}\right)$ $\newline$ (D) $-4\left(2 x^{2}+2 x y+3 y^{2}\right)$

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Math Problems

Grade 7

Identify equivalent linear expressions I

Full solution

Q. Which of the following is equivalent to

-8 x^{2}-8 x y+12 y^{2}

\newline

Choose

1

answer:

\newline

(A)

-4\left(2 x^{2}-2 x y-3 y^{2}\right)

\newline

(B)

-4\left(2 x^{2}-2 x y+3 y^{2}\right)

\newline

(C)

-4\left(2 x^{2}+2 x y-3 y^{2}\right)

\newline

(D)

-4\left(2 x^{2}+2 x y+3 y^{2}\right)

Factor Out GCF: We need to factor out the greatest common factor from the expression $-8x^{2}-8xy+12y^{2}$ . $\newline$ The greatest common factor is $-4$ . $\newline$ Factor out $-4$ from each term in the expression.
Rewrite Expression: After factoring out $-4$ , we rewrite the expression as: $\newline$ $-4(2x^{2} + 2xy - 3y^{2})$ . $\newline$ However, we need to be careful with the signs. The original expression has a negative sign in front of the $xy$ term, so we should have: $\newline$ $-4(2x^{2} - 2xy + 3y^{2})$ .
Check Answer Choices: Now, let's check each answer choice to see which one matches our factored expression: $\newline$ (A) $-4(2x^{2}-2xy-3y^{2})$ does not match because the sign in front of $3y^{2}$ is negative. $\newline$ (B) $-4(2x^{2}-2xy+3y^{2})$ matches our factored expression. $\newline$ (C) $-4(2x^{2}+2xy-3y^{2})$ does not match because the sign in front of $2xy$ is positive. $\newline$ (D) $-4(2x^{2}+2xy+3y^{2})$ does not match because both signs in front of $2xy$ and $3y^{2}$ are positive.