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Algebra 1 : How to multiply a monomial by a polynomial

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #31 : Monomials

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

Possible Answers:

6x^2y+21xy

6xy^2+21xy

15xy

5x^2y+10xy

27xy

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 #32 : Monomials

Expand the following:

3x(x+5)

Possible Answers:

x+15x

3x^2+5

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 #34 : Monomials

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

Possible Answers:

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

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

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 #4692 : Algebra 1

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

Possible Answers:

2x^2+9x-18

-3x^2+9x-18

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

2x^2+3x-6

-3x^4+3x^3-6x^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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Example Question #35 : Monomials

Multiply: 2xy^3(x^2+y^3-xy)

Possible Answers:

2x^2y^3+2xy^6-2x^2y^3

$\frac{2y^3}{x}+2xy^6-2y^2$

2x^3y^3+y^3-xy

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

2x^4y^7

Correct answer:

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

Explanation:

Distribute the monomial throughout the terms of the polynomial.

2xy^3(x^2)+2xy^3(y^3)-2xy^3(xy)

Simplify these terms. When similar bases of a particular power are multiplied, their powers can be added.

The answer is: 2x^3y^3+2xy^6-2x^2y^4

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Example Question #36 : How To Multiply A Monomial By A Polynomial

Multiply with 3x^2+3x+6 .

Possible Answers:

5x^2+3x+6

12x^3+12x

5x^3+5x^2+8x

6x^3+6x^2+12x

6x^2+3x+6

Correct answer:

6x^3+6x^2+12x

Explanation:

Write the expression of the multiplied terms.

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

Distribute the monomial with each term in the polynomial.

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

Simplify this expression.

The answer is: 6x^3+6x^2+12x

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Example Question #37 : How To Multiply A Monomial By A Polynomial

Multiply: -3y^2(x-y-y^2+z)

Possible Answers:

-3xy^2-3y^3-3y^4+3y^2z

-3xy^2+6y^4-3y^2z

-3xy^2+3y^3+3y^4-3y^2z

-3xy^4z

-3xy^2+3y^2+3y^3-3y^2z

Correct answer:

-3xy^2+3y^3+3y^4-3y^2z

Explanation:

Distribute the monomial throughout each term in the polynomial. Be careful with sign changes.

(-3y^2)(x)-(-3y^2)(y)-(-3y^2)(y^2)+(-3y^2)(z)

Simplify each term. The powers of similar bases multiplied by each other can be added.

-3xy^2+3y^3+3y^4-3y^2z

There are no like terms.

The answer is: -3xy^2+3y^3+3y^4-3y^2z

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Algebra 1 : How to multiply a monomial by a polynomial

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #31 : Monomials

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 #32 : Monomials

Example Question #34 : Monomials

Example Question #4692 : Algebra 1

Example Question #35 : Monomials

Example Question #36 : How To Multiply A Monomial By A Polynomial

Example Question #37 : How To Multiply A Monomial By A Polynomial

All Algebra 1 Resources

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