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Common Core: High School - Algebra : Seeing Structure in Expressions

Study concepts, example questions & explanations for Common Core: High School - Algebra

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Example Question #9 : Interpret Complicated Expressions: Ccss.Math.Content.Hsa Sse.A.1b

Identify the equivalent expression.

(2x+7)(2x+7)+9

Possible Answers:

4x^2+49+9

(2x+7)^2-9

4x^2+58

4x^2+40

(2x+7)^2+9

Correct answer:

(2x+7)^2+9

Explanation:

To identify the equivalent expression first identify the different terms that are in the given expression.

(2x+7)(2x+7)+9

$\\\text{Term One}=(2x+7)(2x+7) \\\text{Term Two}=9$

Since there are numerous quantities in term one that are the same, the term can be written in exponential form.

Now, recall the general form for exponents.

$\\a^2=a\cdot a \\(ax)^3=ax\cdot ax\cdot ax$

Term one can be written as,

(2x+7)^2

Combine the two terms together to find an equivalent expression.

(2x+7)^2+9

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Example Question #5 : Interpret Complicated Expressions: Ccss.Math.Content.Hsa Sse.A.1b

Rewrite the following expression:

(x-9)^2

Possible Answers:

(x+9)(x+9)

(x-9)(x-9)

x^2-81

2x^2-81

x^2-9

Correct answer:

(x-9)(x-9)

Explanation:

To rewrite the expression, first identify and interpret the individual parts of the given expression.

Identify the various terms in the expression.

(x-9)^2

$\\\text{Term One}=(x-9)^2$

Now, recall the general form for exponents.

$\\a^2=a\cdot a \\(ax)^3=ax\cdot ax\cdot ax$

Expand the term as follows to get an equivalent expression.

$(x-9)^2=(x-9)\cdot (x-9)$

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Example Question #21 : Seeing Structure In Expressions

Rewrite the following expression:

(3x-1)^2

Possible Answers:

3x^2-1

(3x-1)(3x-1)(3x-1)

6x-2

(3x-1)(3x-1)

9x^2-1

Correct answer:

(3x-1)(3x-1)

Explanation:

To rewrite the expression first identify and interpret the individual parts of the given expression.

Identify the various terms in the expression.

(3x-1)^2

$\\\text{Term One}=(3x-1)^2$

Now, recall the general form for exponents.

$\\a^2=a\cdot a \\(ax)^3=ax\cdot ax\cdot ax$

Expand the term as follows to get an equivalent expression.

$(3x-1)^2=(3x-1)\cdot (3x-1)$

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Example Question #21 : High School: Algebra

Rewrite

2(x+1)^2

Possible Answers:

$2 \cdot (2x + 2)$

$2- (x+1) \cdot (x + 1)$

$2\div (x+1) \cdot (x + 1)$

$2\cdot (x+1) \cdot (x + 1)$

$2+ (x+1) \cdot (x + 1)$

Correct answer:

$2\cdot (x+1) \cdot (x + 1)$

Explanation:

To rewrite the expression, first identify and interpret the individual parts of the given expression.

Identify the various terms in the expression.

2(x+1)^2

$\\\text{Term One}=2 \\\text{Term Two}=(x+1)^2$

Now, recall the general form for exponents.

$\\a^2=a\cdot a \\(ax)^3=ax\cdot ax\cdot ax$

Expand the second term as follows.

$(x+1)^2=(x+1)\cdot (x+1)$

From here, combine the first term with the expanded second term to result in the final solution.

$2\cdot (x+1) \cdot (x + 1)$

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Example Question #1 : Rewriting Expressions Using Its Structure: Ccss.Math.Content.Hsa Sse.A.2

Use the GCF method to rewrite the following expression.

6xy-3y^2

Possible Answers:

3y(2x+y)

3y(2x-y)

3y(2x-y^2)

3y^2(2x-y)

3(2x-y)

Correct answer:

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,

ax+bx=x(a+b)

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

6xy-3y^2

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

The factors that belong to both terms are:

Factoring out the GCF leaves:

(2x-y)

Rewriting the expression, results in the following equivalent expression.

3y(2x-y)

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Example Question #2 : Rewriting Expressions Using Its Structure: Ccss.Math.Content.Hsa Sse.A.2

Use the GCF method to rewrite the following expression.

14x^2y-7y^2

Possible Answers:

7y^2(2x^2-y)

7y(2x-y^2)

7(2x^2-y)

7y(2x^2-y)

7y^2(2x-y)

Correct answer:

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,

ax+bx=x(a+b)

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

14x^2y-7y^2

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

The factors that belong to both terms are:

Factoring out the GCF leaves:

(2x^2-y)

Rewriting the expression, results in the following equivalent expression.

7y(2x^2-y)

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Example Question #21 : Seeing Structure In Expressions

Use the GCF method to rewrite the following expression.

x^2y-7x^2y^2

Possible Answers:

xy(1-7y)

x^2y(1-7y)

x^2(1-7y)

x^2(1-7y^2)

x^2y(x-7y)

Correct answer:

x^2y(1-7y)

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,

ax+bx=x(a+b)

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

x^2y-7x^2y^2

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

The factors that belong to both terms are:

x^2y

Factoring out the GCF leaves:

(1-7y)

Rewriting the expression, results in the following equivalent expression.

x^2y(1-7y)

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Example Question #4 : Rewriting Expressions Using Its Structure: Ccss.Math.Content.Hsa Sse.A.2

Use the GCF method to rewrite the following expression.

2x^2y-4y

Possible Answers:

y(2x^2-2)

2y(x^2-2)

2y(x^2-4)

2(x^2-2)

2y(x^2-2y)

Correct answer:

2y(x^2-2)

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,

ax+bx=x(a+b)

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

2x^2y-4y

$\\\text{Term One}=2x^2y\rightarrow \text{Term One Factors}=1,2,x,x,y \\\text{Term Two}=4y\rightarrow\text{Term Two Factors}=1,2,2,4,y$

The factors that belong to both terms are:

Factoring out the GCF leaves:

(x^2-2)

Rewriting the expression, results in the following equivalent expression.

2y(x^2-2)

Report an Error

Example Question #5 : Rewriting Expressions Using Its Structure: Ccss.Math.Content.Hsa Sse.A.2

Use the GCF method to rewrite the following expression.

2x^2y+y

Possible Answers:

y(2x^2+2)

y(x^2+2)

y(2x^2+1)

2y(2x^2+1)

y(2x^2+y)

Correct answer:

y(2x^2+1)

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,

ax+bx=x(a+b)

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

2x^2y+y

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

The factors that belong to both terms are:

Factoring out the GCF leaves:

(2x^2+1)

Rewriting the expression, results in the following equivalent expression.

y(2x^2+1)

Report an Error

Example Question #6 : Rewriting Expressions Using Its Structure: Ccss.Math.Content.Hsa Sse.A.2

Use the GCF method to rewrite the following expression.

2x^2y+y+3y^3

Possible Answers:

y(2x^2+1+y^2)

y^2(2x^2+1+3y)

y(2x^2+1+3y^2)

y(2x^2+1+3)

y(2x^2+1+3y)

Correct answer:

y(2x^2+1+3y^2)

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,

ax+bx=x(a+b)

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

2x^2y+y+3y^3

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

The factors that belong to both terms are:

Factoring out the GCF leaves:

(2x^2+1+3y^2)

Rewriting the expression, results in the following equivalent expression.

y(2x^2+1+3y^2)

Report an Error

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All Common Core: High School - Algebra Resources

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Common Core: High School - Algebra : Seeing Structure in Expressions

Study concepts, example questions & explanations for Common Core: High School - Algebra

All Common Core: High School - Algebra Resources

Example Questions

Example Question #9 : Interpret Complicated Expressions: Ccss.Math.Content.Hsa Sse.A.1b

Example Question #5 : Interpret Complicated Expressions: Ccss.Math.Content.Hsa Sse.A.1b

Example Question #21 : Seeing Structure In Expressions

Example Question #21 : High School: Algebra

Example Question #1 : Rewriting Expressions Using Its Structure: Ccss.Math.Content.Hsa Sse.A.2

Example Question #2 : Rewriting Expressions Using Its Structure: Ccss.Math.Content.Hsa Sse.A.2

Example Question #21 : Seeing Structure In Expressions

Example Question #4 : Rewriting Expressions Using Its Structure: Ccss.Math.Content.Hsa Sse.A.2

Example Question #5 : Rewriting Expressions Using Its Structure: Ccss.Math.Content.Hsa Sse.A.2

Example Question #6 : Rewriting Expressions Using Its Structure: Ccss.Math.Content.Hsa Sse.A.2

All Common Core: High School - Algebra Resources

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