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Algebra 1 : How to multiply a monomial by a polynomial

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Example Questions

Example Question #41 : Monomials

Multiply:

$\displaystyle 4x(3x+5)$

Possible Answers:

7x + 5 $\displaystyle 7x + 5$

$\displaystyle 12x + 20x$

7x + 20 $\displaystyle 7x + 20$

$12x^{2}+ 5$ $\displaystyle 12x^{2}+ 5$

$\displaystyle 12x^2+ 20x$

Correct answer:

$\displaystyle 12x^2+ 20x$

Explanation:

Use the distributive property and multiply $\displaystyle 4$$\displaystyle x$ by both terms of the binomial:

$\displaystyle 4x (3x+5)$

$\displaystyle 4x (3x) + 4x (5)$

$12x^{2} +20x$ $\displaystyle 12x^{2} +20x$

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Example Question #41 : Monomials

Simplify the following expression.

$3y (-y^{2}-18y+7)$ $\displaystyle 3y (-y^{2}-18y+7)$

Possible Answers:

$2y^{3}-21y^{2}+21y$ $\displaystyle 2y^{3}-21y^{2}+21y$

$-3y^{2}-54y+21$ $\displaystyle -3y^{2}-54y+21$

$-3y^{2}-33y$ $\displaystyle -3y^{2}-33y$

$-y^{2}-15y+7$ $\displaystyle -y^{2}-15y+7$

Correct answer:

Explanation:

Distribute and multiply $\displaystyle 3y$ by each of the terms within the parentheses.

$3y \times -y^{2}=-3y^{3}$ $\displaystyle 3y \times -y^{2}=-3y^{3}$

$3y\times-18y=-54y^{2}$ $\displaystyle 3y\times-18y=-54y^{2}$

$3y\times7=21y$ $\displaystyle 3y\times7=21y$

Regroup the resulting terms

$-3y^{3}-54y^{2}+21y$ $\displaystyle -3y^{3}-54y^{2}+21y$

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Example Question #42 : Monomials

Simplify the following expression.

$\displaystyle 3x(-4x+7)$

Possible Answers:

$12x^{2}-21x$ $\displaystyle 12x^{2}-21x$

$-x^{2}+10x$ $\displaystyle -x^{2}+10x$

$-7x^{2}+4x$ $\displaystyle -7x^{2}+4x$

None of the other answers.

Correct answer:

Explanation:

Distribute $\displaystyle 3x$ to each of the terms within the parentheses.

$3x\times-4x=-12x^{2}$ $\displaystyle 3x\times-4x=-12x^{2}$

$3x\times7=21x$ $\displaystyle 3x\times7=21x$

Putting it back together...

$-12x^{2}+21x$ $\displaystyle -12x^{2}+21x$

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Example Question #44 : How To Multiply A Monomial By A Polynomial

Simplify the following expression.

$-2x^{2}(2x^{2}-11x)$ $\displaystyle -2x^{2}(2x^{2}-11x)$

Possible Answers:

$4x^{4}-22x^{3}$ $\displaystyle 4x^{4}-22x^{3}$

$x^{4}-13x^{3}$ $\displaystyle x^{4}-13x^{3}$

22x $\displaystyle 22x$

-11x $\displaystyle -11x$

Correct answer:

Explanation:

$-2x^{2}(2x^{2}-11x)$ $\displaystyle -2x^{2}(2x^{2}-11x)$

Distribute $-2x^{2}$ $\displaystyle -2x^{2}$ to each term within parentheses.

$-2x^{2}(2x^{2})=-4x^{4}$ $\displaystyle -2x^{2}(2x^{2})=-4x^{4}$

$-2x^{2}(-11x)=22x^{3}$ $\displaystyle -2x^{2}(-11x)=22x^{3}$

Putting it back together...

$-4x^{4}+22x^{3}$ $\displaystyle -4x^{4}+22x^{3}$

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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 #41 : Monomials

Example Question #41 : Monomials

Example Question #42 : Monomials

Example Question #44 : How To Multiply A Monomial By A Polynomial

All Algebra 1 Resources

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