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Algebra 1 : Variables

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Example Questions

Example Question #451 : Variables

$3x(x^{2}+3x-2)$

Multiply the polynomial by the monomial.

Possible Answers:

$x^{3}+3x^{2}-2x$

$3x^{2}-9x-6$

$3x^{3}+9x^{2}-6x$

$x^{2}+3x-2+3x$

$3x^{2}+9x-6$

Correct answer:

$3x^{3}+9x^{2}-6x$

Explanation:

When multiplying a polynomial and a monomial, distribute the monomial into the polynomial:

$3x(x^{2}+3x-2) {\color{Blue} \rightarrow } {\color{Blue} 3x\cdot x^{2} + 3x\cdot 3x - 3x\cdot 2}$

Then simplify and the answer is: $3x^{3}+9x^{2}-6x$

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Example Question #452 : Variables

$4x^{3}(x^{4}+7x^{2}-12x)$

Multiply the polynomial by the monomial.

Possible Answers:

$x^{7}+7x^{5}+12x^{2}$

$x^{3}+7x^{3}+12x^{3}$

$4x^{3}+28x^{3}+48x^{3}$

$4x^{7}+28x^{5}+48x^{4}$

$4x^{4}+28x^{2}+48x$

Correct answer:

$4x^{7}+28x^{5}+48x^{4}$

Explanation:

When multiplying a polynomial and a monomial, distribute the monomial into the polynomial:

$4x^{3}(x^{4}+7x^{2}-12x) {\color{Blue} \rightarrow } {\color{Blue} 4x^{3}}\cdot x^{4} + {\color{Blue} 4x^{3}}\cdot 7x^{2} - {\color{Blue} 4x^{3}}\cdot 12x$

Then simplify and the answer is: $4x^{7}+28x^{5}+48x^{4}$

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Example Question #453 : Variables

Multiply: 2x(x^2-3x+4)

Possible Answers:

2x^2-6x+8

2x^3-2x

2x^3-6x^2+8x

2x^3-14x

4x^3

Correct answer:

2x^3-6x^2+8x

Explanation:

Distribute the term through every term inside the parentheses.

(2x)(x^2)+(2x)(-3x)+(2x)(4)

Simplify and multiply out each term.

(2x)(x^2)+(2x)(-3x)+(2x)(4) = 2x^3-6x^2+8x

The answer is: 2x^3-6x^2+8x

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Example Question #451 : Variables

$3xy\cdot (2x+7)$

Possible Answers:

6xy^2+21xy

15xy

27xy

6x^2y+21xy

5x^2y+10xy

Correct answer:

6x^2y+21xy

Explanation:

Distribute the minimal into the binomial to evaluate:

$3xy\cdot (2×+7)=6x^2y+21xy$

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Example Question #455 : Variables

Multiply: 9x(3x^3+2x+1)

Possible Answers:

3x^3+11x+1

27x^4+18x^2+9x

12x^4+11x^2+10x

12x^4+18x^2+9x

27x^3+11x^2+9x

Correct answer:

27x^4+18x^2+9x

Explanation:

In order to simplify this expression, we must distribute the term among all the terms inside the parentheses. If there are any like terms existent afterward, we will need to combine like terms.

9x(3x^3+2x+1)=9x(3x^3)+9x(2x)+9x(1)

=27x^4+18x^2+9x

The answer is: 27x^4+18x^2+9x

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Example Question #456 : Variables

Multiply: 2x(x+5)

Possible Answers:

3x + 10

2x^2 + 10x

2x + 10

2x^2 + 5

Correct answer:

2x^2 + 10x

Explanation:

use the distributive property: 2x*x + 2x* 5

x*x = x^2 so 2x*x = 2x^2

2*5 = 10 so 2x*5 = 10x

The answer is 2x^2 + 10x

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Example Question #457 : Variables

Multiply: 7x (x^2+3x-1)

Possible Answers:

7x^3+x^2-x

21x^2-7x

14x^3+21x^2-x

x^3-9x-1

7x^3+21x^2-7x

Correct answer:

7x^3+21x^2-7x

Explanation:

Distribute the throughout each term in the parentheses.

7x (x^2+3x-1)= (7x)(x^2) + (7x)(3x)+(7x)(-1)

Simplify all terms on the right.

The answer is: 7x^3+21x^2-7x

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Example Question #452 : Variables

Expand the following:

3x(x+5)

Possible Answers:

3x^2+5

x+15x

3x^2+15x

Correct answer:

3x^2+15x

Explanation:

To expand this, you must distribute the 3x to each of the terms in the parenthesis. Therefore, you get the following:

3x(x+5)

(3x)(x)+(3x)(5)

3x^2+15x

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Example Question #459 : Variables

Multiply: 3x^4(x^2+x-6)

Possible Answers:

$4x^{8}+4x^{4}-9x^4$

$3x^{8}+3x^{4}-18x^4$

3x^4+x^2+x-6

$4x^{6}+4x^{5}-9x^4$

$3x^{6}+3x^{5}-18x^4$

Correct answer:

$3x^{6}+3x^{5}-18x^4$

Explanation:

Multiply by distributing the 3x^4 term across each term in the parentheses.

3x^4(x^2+x-6) = (3x^4)(x^2)+(3x^4)(x)+(3x^4)(-6)

Expand each term. When multiplying similar bases with a power, their powers can be added.

$3x^{4+2}+3x^{4+1}-18x^4$

Simplify.

The answer is: $3x^{6}+3x^{5}-18x^4$

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Example Question #460 : Variables

Multiply: 3x^2(-x^2+3x-6)

Possible Answers:

-3x^2+9x-18

2x^2+3x-6

-3x^4+3x^3-6x^2

2x^2+9x-18

-3x^4+9x^3-18x^2

Correct answer:

-3x^4+9x^3-18x^2

Explanation:

To simplify this expression, simply distribute the monomial throughout the terms inside the polynomial.

3x^2(-x^2+3x-6) = (3x^2)(-x^2)+(3x^2)(3x)+(3x^2)(-6)

Simplify all the terms. When multiplying bases with a power, it is the same as adding the powers.

The answer is: -3x^4+9x^3-18x^2

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Algebra 1 : Variables

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #451 : Variables

Example Question #452 : Variables

Example Question #453 : Variables

Example Question #451 : Variables

Example Question #455 : Variables

Example Question #456 : Variables

Example Question #457 : Variables

Example Question #452 : Variables

Example Question #459 : Variables

Example Question #460 : Variables

All Algebra 1 Resources

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