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Flashcards: Rewriting Expressions Using its Structure: CCSS.Math.Content.HSA-SSE.A.2

Use the GCF method to rewrite the following expression.

$\displaystyle 6xy-3y^2$

$\displaystyle 3y(2x+y)$

$\displaystyle 3y(2x-y^2)$

$\displaystyle 3y(2x-y)$

3(2x-y) $\displaystyle 3(2x-y)$

$\displaystyle 3y^2(2x-y)$

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Flashcards: Rewriting Expressions Using its Structure: CCSS.Math.Content.HSA-SSE.A.2

Use the GCF method to rewrite the following expression.

$\displaystyle 6xy-3y^2$

$\displaystyle 3y(2x+y)$

$\displaystyle 3y(2x-y^2)$

$\displaystyle 3y(2x-y)$

3(2x-y) $\displaystyle 3(2x-y)$

$\displaystyle 3y^2(2x-y)$

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Flashcards: Rewriting Expressions Using its Structure: CCSS.Math.Content.HSA-SSE.A.2

Use the GCF method to rewrite the following expression.

$\displaystyle 6xy-3y^2$

Your answer:

$\displaystyle 3y(2x+y)$

Your answer:

$\displaystyle 3y(2x-y^2)$

Your answer:

3(2x-y) $\displaystyle 3(2x-y)$

Your answer:

$\displaystyle 3y^2(2x-y)$

Correct answer:

$\displaystyle 3y(2x-y)$

Explanation:

To use the GCF method to rewrite the expression, first recall what the GCF method means.

GCF stands for 'Greatest Common Factor' which means the largest factor or factors that belong to all terms in the expression.

In general terms,

$\displaystyle ax+bx=x(a+b)$

Looking at the expression in question, break down each term into its factors.

$\displaystyle 6xy-3y^2$

$\\\text{Term One}=6xy\rightarrow \text{Term One Factors}=1,2,3,6,x,y \\\text{Term Two}=3y^2\rightarrow\text{Term Two Factors}=1,3,y,y$ $\displaystyle \\\text{Term One}=6xy\rightarrow \text{Term One Factors}=1,2,3,6,x,y \\\text{Term Two}=3y^2\rightarrow\text{Term Two Factors}=1,3,y,y$

The factors that belong to both terms are:

$\displaystyle 3y$

Factoring out the GCF leaves:

(2x-y) $\displaystyle (2x-y)$

Rewriting the expression, results in the following equivalent expression.

$\displaystyle 3y(2x-y)$

Flashcards: Rewriting Expressions Using its Structure: CCSS.Math.Content.HSA-SSE.A.2

Use the GCF method to rewrite the following expression.

$\displaystyle 14x^2y-7y^2$

$\displaystyle 7y(2x-y^2)$

$\displaystyle 7y^2(2x^2-y)$

$\displaystyle 7(2x^2-y)$

$\displaystyle 7y(2x^2-y)$

$\displaystyle 7y^2(2x-y)$

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Flashcards: Rewriting Expressions Using its Structure: CCSS.Math.Content.HSA-SSE.A.2

Use the GCF method to rewrite the following expression.

$\displaystyle 14x^2y-7y^2$

Your answer:

$\displaystyle 7y(2x-y^2)$

Your answer:

$\displaystyle 7y^2(2x^2-y)$

Your answer:

$\displaystyle 7(2x^2-y)$

Your answer:

$\displaystyle 7y^2(2x-y)$

Correct answer:

$\displaystyle 7y(2x^2-y)$

Explanation:

To use the GCF method to rewrite the expression, first recall what the GCF method means.

GCF stands for 'Greatest Common Factor' which means the largest factor or factors that belong to all terms in the expression.

In general terms,

$\displaystyle ax+bx=x(a+b)$

Looking at the expression in question, break down each term into its factors.

$\displaystyle 14x^2y-7y^2$

$\\\text{Term One}=14x^2y\rightarrow \text{Term One Factors}=1,2,7,14,x,x,y \\\text{Term Two}=7y^2\rightarrow\text{Term Two Factors}=1,7,y,y$ $\displaystyle \\\text{Term One}=14x^2y\rightarrow \text{Term One Factors}=1,2,7,14,x,x,y \\\text{Term Two}=7y^2\rightarrow\text{Term Two Factors}=1,7,y,y$

The factors that belong to both terms are:

$\displaystyle 7y$

Factoring out the GCF leaves:

$\displaystyle (2x^2-y)$

Rewriting the expression, results in the following equivalent expression.

$\displaystyle 7y(2x^2-y)$

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Flashcards: Rewriting Expressions Using its Structure: CCSS.Math.Content.HSA-SSE.A.2

All Common Core: High School - Algebra Resources

Flashcards: Rewriting Expressions Using its Structure: CCSS.Math.Content.HSA-SSE.A.2

Flashcards: Rewriting Expressions Using its Structure: CCSS.Math.Content.HSA-SSE.A.2

Flashcards: Rewriting Expressions Using its Structure: CCSS.Math.Content.HSA-SSE.A.2

Flashcards: Rewriting Expressions Using its Structure: CCSS.Math.Content.HSA-SSE.A.2

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