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Algebra 1 : How to multiply a monomial by a polynomial

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Example Questions

Example Question #1 : How To Multiply A Monomial By A Polynomial

$Expand \;x(x-2)$

Possible Answers:

2x -2

$x^{2}$

$x^{2}-2x$

$x^{2}+2x$

Correct answer:

$x^{2}-2x$

Explanation:

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Example Question #2 : How To Multiply A Monomial By A Polynomial

Evaluate.

$ab(ab^{2}+4a-b)$

Possible Answers:

$a^{2}b^{2}+4a-b$

$4a^{3}b^{2}$

2ab+4a-b

$a^{2}b^{3}+4a^{2}b-ab^{2}$

Correct answer:

$a^{2}b^{3}+4a^{2}b-ab^{2}$

Explanation:

$ab(ab^{2}+4a-b)$

Using the distributive property you are simply going to share the term , with every term in the poynomial

$ab\cdot ab^{2}+ ab\cdot 4a- ab\cdot b$

Now because we are multiplying like variables we can add the exponents, to simplify each expression

$a^{2}b^{3}+4a^{2}b-ab^{2}$

This will be our final answer because we can not add terms unless they are 'like' meaning they contain the same elements and degrees.

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Example Question #1 : How To Multiply A Monomial By A Polynomial

Multiply:

$-3t ^{2} ( 2t ^{2} - 5t + 7)$

Possible Answers:

$-6 t ^{4} - 15t ^{3} +21t ^{2}$

$-6 t ^{4} + 5t ^{3} -7t ^{2}$

$-6 t ^{4} - 5t ^{3} +7t ^{2}$

$-6 t ^{4} + 15t ^{3} -21t ^{2}$

$-6 t ^{4} - 15t ^{3} -21t ^{2}$

Correct answer:

$-6 t ^{4} + 15t ^{3} -21t ^{2}$

Explanation:

$-3t ^{2} ( 2t ^{2} - 5t + 7)$

$= -3t ^{2} \cdot 2t ^{2} - \left (-3t ^{2} \right )\cdot 5t +\left (-3t ^{2} \right )\cdot 7$

$= -3t ^{2} \cdot 2t ^{2} + 3t ^{2} \cdot 5t -3t ^{2}\cdot 7$

$= -3\cdot 2 \cdot t ^{2} \cdot t ^{2} + 3\cdot 5 \cdot t ^{2} \cdot t -3\cdot 7 \cdot t ^{2}$

$= -6 \cdot t ^{2+2} + 15\cdot t ^{2+1} -21 \cdot t ^{2}$

$= -6 t ^{4} + 15t ^{3} -21t ^{2}$

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Example Question #3 : How To Multiply A Monomial By A Polynomial

Simplify the following:

$(2p^{2})(4x+p)$

Possible Answers:

$(8xp)^{2}+2p^{3}$

$8xp^{2}+2p^{3}$

None of the other answers

$6xp^{2}+3p^{3}$

$8xp^{2}+2p^{2}$

Correct answer:

$8xp^{2}+2p^{3}$

Explanation:

Distribute the $2p^{2}$ to each term in the parentheses in the other polynomial.

$2p^{2}(4x)=8xp^{2}$

$2p^{2}(p)=2p^{3}$

Putting the results back together

$(2p^{2})(4x+p)=8xp^{2}+2p^{3}$

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Example Question #4 : Monomials

Multiply:

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

Possible Answers:

12x^3-8x^2+16x

-12x^3+8x^2-16x

-12x^3-8x^2-16x

-12x^3-8x^2+16x

Correct answer:

-12x^3+8x^2-16x

Explanation:

Multiply each term of the polynomial by -4x . Be careful to distribute the negative sign.

(-4x)(3x^2)=-12x^3

(-4x)(-2x)=8x^2

(-4x)(4)=-16x

Add the individual terms together:

-12x^3+8x^2+(-16x)=12x^3+8x^2-16x

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Example Question #3 : Monomials

Simplify the following

$(7y)(7t-3y^{3} + 2)$

Possible Answers:

$49yt-21y^{2} +14y$

$14yt-21y^{4} +14y$

$14yt-10y^{4} +14y$

$49yt-21y^{4} +14y$

$28y-21y^{4} +14t$

Correct answer:

$49yt-21y^{4} +14y$

Explanation:

Distribute to each term in the parentheses in the polynomial

7y(7t)=49yt

$7y(-3y^{3})=-21y^{4}$

7y(2)=14y

Combine the results

$(7y)(7t-3y^{3} + 2)=49yt-21y^{4} +14y$

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Example Question #3 : How To Multiply A Monomial By A Polynomial

Expand the expression by multiplying the terms.

$\small (x-4)(x+2)(2x-5)$

Possible Answers:

$\small 2x^3+x^2-26x+40$

$\small 2x^3+9x^2-6x+40$

$\small 2x^3-9x^2-6x+40$

$\small 2x^3-x^2-26x+40$

Correct answer:

$\small 2x^3-9x^2-6x+40$

Explanation:

$\small (x-4)(x+2)(2x-5)$

When multiplying, the order in which you multiply does not matter. Let's start with the first two monomials.

(x-4)(x+2)

Use FOIL to expand.

x^2+2x-4x-8=x^2-2x-8

Now we need to multiply the third monomial.

$\small (x-4)(x+2)(2x-5)=(x^2-2x-8)(2x-5)$

Similar to FOIL, we need to multiply each combination of terms.

2x(x^2-2x-8)+(-5)(x^2-2x-8)

2x^3-4x^2-16x-5x^2+10x+40

Combine like terms.

2x^3-9x^2-6x+40

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Example Question #3 : Simplifying Expressions

Find the product:

$\small 7n(8n-2)$

Possible Answers:

$\small n^2-14n$

$\small n^2+14$

$\small 56n^2-14n$

$\small n-14$

Correct answer:

$\small 56n^2-14n$

Explanation:

First, mulitply the mononomial by the first term of the polynomial:

$\small 7n\times8n\ = 56n^2$

Second, multiply the monomial by the second term of the polynomial:

$\small 7n\times (-2)\ = -14n$

Add the terms together:

$\small 56n^2\ +\ (-14n)\ = 56n^2-14n$

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Example Question #2 : Simplifying Expressions

Expand: 8x(3x+7)

Possible Answers:

24x + 56

24x^2 + 56

24x^2 + 56x

11x^2 + 15x

11x + 15

Correct answer:

24x^2 + 56x

Explanation:

To expand, multiply 8x by both terms in the expression (3x + 7).

8x multiplied by 3x is 24x².

8x multiplied by 7 is 56x.

Therefore, 8x(3x + 7) = 24x² + 56x.

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Example Question #4 : How To Multiply A Monomial By A Polynomial

Write 4x^2(3x^2+2x+4) as a polynomial.

Possible Answers:

$12x^{2}+8x+16$

$36x^{2}$

$7x^{4}+6x^{3}+8x^{2}$

$12x^{4}+8x^{2}+8x$

$12x^{4}+8x^{3}+16x^{2}$

Correct answer:

$12x^{4}+8x^{3}+16x^{2}$

Explanation:

We need to distribute the 4x² through the terms in the parentheses:

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

This becomes 12x^4+8x^3+16x^2 .

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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 #1 : How To Multiply A Monomial By A Polynomial

Example Question #2 : How To Multiply A Monomial By A Polynomial

Example Question #1 : How To Multiply A Monomial By A Polynomial

Example Question #3 : How To Multiply A Monomial By A Polynomial

Example Question #4 : Monomials

Example Question #3 : Monomials

Example Question #3 : How To Multiply A Monomial By A Polynomial

Example Question #3 : Simplifying Expressions

Example Question #2 : Simplifying Expressions

Example Question #4 : How To Multiply A Monomial By A Polynomial

All Algebra 1 Resources

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