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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #444 : Variables

Which of the following is equivalent to the given statement?

4b(b^3-8+b^2)

Possible Answers:

4b^4-4b^3+32b

4b^4+4b^3-32b

b^4+b^3-8b

4b^3+4b^2-32

Correct answer:

4b^4+4b^3-32b

Explanation:

Which of the following is equivalent to the given statement?

4b(b^3-8+b^2)

This question asks us to distribute a monomial through a polynomial. To do so, we need to multiply the monomial (4b) by each part of the polynomial in parentheses.

4b(b^3-8+b^2)=4b(b^3)+4b(-8)+4b(b^2)

4b(b^3)+4b(-8)+4b(b^2)=4b^4-32b+4b^3

So our answer in standard form is as follows:

4b^4+4b^3-32b

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Example Question #4682 : Algebra 1

$x^{2}(2x^{3}+6x-4)$

Multiply the polynomial by the monomial.

Possible Answers:

$2x^{3}+6x^{2}-4x$

$2x^{3}+6x-4$

$2x^{3}+6x-4+x^{2}$

$2x^{2}+6x^{3}-4x^{2}$

$2x^{5}+6x^{3}-4x^{2}$

Correct answer:

$2x^{5}+6x^{3}-4x^{2}$

Explanation:

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

$x^{2}(2x^{3}+6x-4) {\color{Blue} \rightarrow } {\color{Blue} x^{2}\cdot 2x^{3} + x^{2}\cdot 6x - x^{2}\cdot 4}$

Then simplify and the answer is: $2x^{5}+6x^{3}-4x^{2}$

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Example Question #4683 : Algebra 1

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

Multiply the polynomial by the monomial.

Possible Answers:

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

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

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

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

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

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 #4682 : Algebra 1

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

Multiply the polynomial by the monomial.

Possible Answers:

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

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

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

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

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

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 #4683 : Algebra 1

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

Possible Answers:

2x^3-2x

2x^2-6x+8

2x^3-14x

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

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 #4681 : Algebra 1

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

Possible Answers:

27xy

5x^2y+10xy

15xy

6xy^2+21xy

6x^2y+21xy

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 #32 : How To Multiply A Monomial By A Polynomial

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

Possible Answers:

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

3x^3+11x+1

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

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

12x^4+18x^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 #33 : How To Multiply A Monomial By A Polynomial

Multiply: 2x(x+5)

Possible Answers:

3x + 10

2x^2 + 5

2x^2 + 10x

2x + 10

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 #34 : How To Multiply A Monomial By A Polynomial

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

Possible Answers:

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

14x^3+21x^2-x

21x^2-7x

x^3-9x-1

7x^3+x^2-x

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 #4682 : Algebra 1

Expand the following:

3x(x+5)

Possible Answers:

3x^2+15x

3x^2+5

x+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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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #444 : Variables

Example Question #4682 : Algebra 1

Example Question #4683 : Algebra 1

Example Question #4682 : Algebra 1

Example Question #4683 : Algebra 1

Example Question #4681 : Algebra 1

Example Question #32 : How To Multiply A Monomial By A Polynomial

Example Question #33 : How To Multiply A Monomial By A Polynomial

Example Question #34 : How To Multiply A Monomial By A Polynomial

Example Question #4682 : Algebra 1

All Algebra 1 Resources

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