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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 #22 : Simplifying Expressions

Find the product: $5g(g^{2} - 4)$

Possible Answers:

$5g^{2}-20$

$5g^{3}-20$

$5g^{2}-20g$

$5g^{3}-20g$

$-16g^{2}$

Correct answer:

$5g^{3}-20g$

Explanation:

times $g^{2}$ gives us $5g^{3}$ , while times 4 gives us 20g . So it equals $5g^{3}-20g$ .

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Example Question #23 : Simplifying Expressions

Distribute:

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

Possible Answers:

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

$8x^{3}+3x^{2}-4x$

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

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

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

Correct answer:

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

Explanation:

Be sure to distribute the along with its coefficient.

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Example Question #33 : Simplifying Expressions

Simplify the following expression.

$4x(3x^{2}+x+10)$

Possible Answers:

$7x^{3}+4x^{2}+14x$

$11x^{2}+40x$

None of the other answers

$12x^{2}+14x$

Correct answer:

Explanation:

Distribute the outside term into the parentheses.

$4x(3x^{2}+x+10)=(4x*3x^{2})+(4x *x) +(4x* 10)$

Simplify each distributed factor into one expression.

$12x^{3}+4x^{2}+40x$

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Example Question #32 : Simplifying Expressions

Simplify the following expression.

$5y(3y^{3}-2y+9)$

Possible Answers:

$15y^{3}+35y$

None of the other answers.

$8y^{4}-7y^{2}+14y$

$8y^{4}+3y^{2}+14y$

Correct answer:

Explanation:

Distribute the outside term into the parentheses.

$5y(3y^{3}-2y+9)=(5y* 3y^{3})- (5y* 2y) + (5y*9)$

Simplify each distributed factor into one expression.

$15y^{4}-10y^{2}+45y$

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Example Question #23 : Intermediate Single Variable Algebra

$\textup{What is the product of }2x\textup{ and }3x^{2}-5x+2\textup{?}$

Possible Answers:

$6x^{2}-10x+4$

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

$6x^{3}-10x^{2}+4x$

$3x^{2}-10x^{2}+2$

$6x^{3}+10x^{2}+4x$

Correct answer:

$6x^{3}-10x^{2}+4x$

Explanation:

$\textup{Distribute: Multiply each term in the polynomial by }2x:$

$2x\left ( 3x^{2}-5x+2\right )=2x(3x^{2})+2x(-5x)+2x(2)$

$6x^{3}-10x^{2}+4x$

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Example Question #21 : Polynomials

$4x^{2}y\left ( 2xy + 6xy^{2} + 3y^{{3}}\right ) =$

Possible Answers:

$32x^{3}y^{3} + 12x^{2}y^{4}$

$8x^{3}y^{2} + 24x^{3}y^{3} + 12x^{4}y^{2}$

$8x^{2}y^{2} + 16x^{2}y^{3} + 24x^{2}y^{4}$

$8x^{3}y^{2} + 24x^{3}y^{3} + 12x^{2}y^{4}$

$8x^{3}y^{2} + 24x^{2}y^{2} + 12x^{3}$

Correct answer:

$8x^{3}y^{2} + 24x^{3}y^{3} + 12x^{2}y^{4}$

Explanation:

Use the distributive property to obtain each term:

$4x^{2}y\left ( 2xy + 6xy^{2} + 3y^{{3}}\right ) =$

$4x^{2}y(2xy) + 4x^{2}y(6xy^{2}) + 4x^{2}y(3y^{3}) =$

$8x^{3}y^{2} + 24x^{3}y^{3} + 12x^{2}y^{4}$

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Example Question #433 : Variables

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

Possible Answers:

6x^6+12x^5+9x^4

9x^4-12x^5+6x^6

9x^5-12x^4+6x^6

-9x^4+12x^5+6x^6

Correct answer:

9x^4-12x^5+6x^6

Explanation:

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Example Question #441 : Variables

Multiply: 3x^2(4x^3 - 5)

Possible Answers:

12x^5 - 15x^2

-3x^2

7x^5 -2x^2

12x^6 -5x^2

Correct answer:

12x^5 - 15x^2

Explanation:

To multiply this expression, multiply the monomial times both terms in the binomial.

First we will multiply 3x^2 * 4x^3 , which represents 3*x*x * 4*x*x*x . This is why we evalute this by multiplying 3*4 = 12 and adding the exponents for x to get x^5 .

Now multiply 3x^2 * -5 = -15x^2 .

Our answer is just 12x^5 - 15x^2 .

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Example Question #17 : Monomials

Multiply x^3+2x^2+4x+8 by .

Possible Answers:

x^9y+6x^6y+12x^3y+24y

x^3y+6x^2y+12xy+24y

3x^3y+5x^2y+12xy+24y

3x^3y+6x^2y+12xy+24y

x^6y+6x^5y+12x^4y+24x^3y

Correct answer:

3x^3y+6x^2y+12xy+24y

Explanation:

To multiply a monomial by a polynomial, you simply multiply the monomial by each term in the polynomial. In this case that means that the solution is to multiply everything by . The answer becomes 3x^3y+6x^2y+12xy+24y .

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Example Question #11 : How To Multiply A Monomial By A Polynomial

Multiply: xy(x^2+x)

Possible Answers:

2x^2y+2xy

2x^2+3x+y

2x^2y+2xy

3xy+2x

x^3y+x^2y

Correct answer:

x^3y+x^2y

Explanation:

When similar bases are multiplied, their powers can be added. Distribute the monomial through the polynomial in the parentheses.

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

The answer is: x^3y+x^2y

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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 #22 : Simplifying Expressions

Example Question #23 : Simplifying Expressions

Example Question #33 : Simplifying Expressions

Example Question #32 : Simplifying Expressions

Example Question #23 : Intermediate Single Variable Algebra

Example Question #21 : Polynomials

Example Question #433 : Variables

Example Question #441 : Variables

Example Question #17 : Monomials

Example Question #11 : How To Multiply A Monomial By A Polynomial

All Algebra 1 Resources

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