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Algebra 1 : How to multiply a monomial by a polynomial

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Example Questions

Example Question #21 : Monomials

Simplify:

$5 \times 10xy$

Possible Answers:

The answers provided do not show the correct simplificaiton.

$50x \times 50y$

$15x \times y$

5xy

50xy

Correct answer:

50xy

Explanation:

When multiplying a whole number by a polynomial, we simply multiply that number by whatever coefficient is present in front of the variables of the polynomial. We then maintain the variables in the simplified expression.

$10 \times 5 = 50$

50xy

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Example Question #4673 : Algebra 1

Simplify the following expression:

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

Possible Answers:

$6x^{3}y^{2}+9xy^{3}-21xy$

$5x^{2}y+6xy^{2}-10xy$

$6x^{2}y+9y^{2}-21xy$

$6x^{2}y+9xy^{2}-21xy$

$\frac{2}{3}x+y-\frac{7}{3}xy$

Correct answer:

$6x^{3}y^{2}+9xy^{3}-21xy$

Explanation:

Use the distributive property to multiply the monomial and polynomial.

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

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

$6x^{3}y^{2}+9xy^{3}-21xy$

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Example Question #443 : Variables

Evaluate the expression:

$5x(x^{2}-3x+1)$

Possible Answers:

$x^{2}+2x+1$

$-10x^{2}+5x$

$5x^{3}-15x^{2}+5x$

$5x^{3}+15x^{2}+5x$

$5x^{3}-3x+1$

Correct answer:

$5x^{3}-15x^{2}+5x$

Explanation:

Multipying a monomial and trinomial boils down to distributing the monomial amongst all the parts of the trinomial as such:

$5x(x^{2}-3x+1)=(5x\cdotx^{2})+(5x\cdot-3x)+(5x\cdot1)$

After some cleanup we get:

$5x^{3}-15x^{2}+5x$

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Example Question #4676 : Algebra 1

Multiply: $4r(3r^{2}+2r-12)$

Possible Answers:

$12r^{3}-40r$

$12r^{3}+20r^{2}-48r$

$12r^{3}+8r^{2}-48r$

$4r^{3}+8r^{2}-48r$

$20r^{2}-48r$

Correct answer:

$12r^{3}+8r^{2}-48r$

Explanation:

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

All we need to do here is multiply every term within the polynomial $(3r^{2}+2r-12)$ by the monomial on the outside of the parentheses: .

To do this we need to multiply every term by and by . Remember that when we multiply by a variable (in this case ), we need to add to each of the exponents.

So this leaves us with $12r^{3}+8r^{2}-48r$ .

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Example Question #4677 : Algebra 1

Divide: $\frac{x^2+x}{2x^2-2x}$

Possible Answers:

$\textup{The fraction is already simplified to its fullest.}$

$\frac{1}{x-1}$

$\frac{x+1}{2x-2}$

$-\frac{1}{2}$

Correct answer:

$\frac{x+1}{2x-2}$

Explanation:

To divide this, we must pull out a common factor from the numerator and denominator.

The common factor from the numerator is only .

The common factor from the denominator is .

$\frac{x^2+x}{2x^2-2x} = \frac{x\cdot(x+1)}{2\cdot x\cdot (x-1)}$

The only term that will cancel is the . We cannot cancel the inside x+1 and x-1 terms because they are different entities of a quantity.

$\frac{x\cdot(x+1)}{2\cdot x\cdot (x-1)} = \frac{x+1}{2(x-1)} = \frac{x+1}{2x-2}$

The answer is: $\frac{x+1}{2x-2}$

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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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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 #21 : Monomials

Example Question #4673 : Algebra 1

Example Question #443 : Variables

Example Question #4676 : Algebra 1

Example Question #4677 : Algebra 1

Example Question #444 : Variables

Example Question #4682 : Algebra 1

Example Question #4683 : Algebra 1

Example Question #4682 : Algebra 1

Example Question #4683 : Algebra 1

All Algebra 1 Resources

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