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Algebra 1 : Monomials

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Example Questions

Example Question #461 : Variables

Multiply:

4x(3x+5)

Possible Answers:

7x + 5

12x^2+ 20x

7x + 20

12x + 20x

$12x^{2}+ 5$

Correct answer:

12x^2+ 20x

Explanation:

Use the distributive property and multiply by both terms of the binomial:

4x (3x+5)

4x (3x) + 4x (5)

$12x^{2} +20x$

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Example Question #42 : How To Multiply A Monomial By A Polynomial

Simplify the following expression.

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

Possible Answers:

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

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

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

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

Correct answer:

Explanation:

Distribute and multiply by each of the terms within the parentheses.

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

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

$3y\times7=21y$

Regroup the resulting terms

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

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Example Question #43 : How To Multiply A Monomial By A Polynomial

Simplify the following expression.

3x(-4x+7)

Possible Answers:

$-x^{2}+10x$

None of the other answers.

$12x^{2}-21x$

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

Correct answer:

Explanation:

Distribute to each of the terms within the parentheses.

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

$3x\times7=21x$

Putting it back together...

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

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

Simplify the following expression.

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

Possible Answers:

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

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

22x

-11x

Correct answer:

Explanation:

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

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

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

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

Putting it back together...

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

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Example Question #1 : How To Divide Monomial Quotients

Evaluate

$\frac{(12w^{2}-15w+21w^{3})}{3w}$

Possible Answers:

$2w^{2}+4w-5$

$7w^{2}+4w-5$

$2w^{2}-4w+5$

$-1+7w^{2}$

Correct answer:

$7w^{2}+4w-5$

Explanation:

$\frac{(12w^{2}-15w+21w^{3})}{3w}$

When dividing a polynomial by a monomial, we can use a divison called, term-by-term, dividing each of the top terms by the monomial.

$\frac{12w^{2}}{3w}-\frac{15w}{3w}+\frac{21w^{3}}{3w}$

Simplify.

$4w-5+7w^{2}$

Rewrite it with the leading coefficent first,

Final Answer: $7w^{2}+4w-5$

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Example Question #2 : How To Divide Monomial Quotients

Simplify the fraction to its lowest terms:

$\frac{18x^4y^3z}{6xy^2z^3}$

Possible Answers:

3x^3yz^2

3x^5y^5z^4

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

3x^3yz^2

12x^3yz^2

Correct answer:

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

Explanation:

The first step is to divide the constants, 18 and 6, by the LCM, 6, to get 3. When dividing variables, if the variable is present in the numerator and denominator, subtract the exponent found in the numerator by the exponent in the denominator.

For , you have 4-1=3 .

For , you have 3-2=1 .

For , you have 1-3=-2 .

Then write the simplified answer as one term:

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

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Example Question #1 : How To Divide Monomial Quotients

Divide:

$\frac{9x^4+6x^3-12x}{3x}$

Possible Answers:

6x^3+3x^2+9

6x^3+3x^2-9

3x^3+2x^2+4

3x^3+2x^2-4

Correct answer:

3x^3+2x^2-4

Explanation:

$\frac{9x^4+6x^3-12x}{3x}=\frac{9x^4}{3x}+\frac{6x^3}{3x}-\frac{12x}{3x}=3x^3+2x^2-4$

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Example Question #1 : How To Divide Monomial Quotients

Siimplify:

$\frac{2x^{2}y^{3}z - 6xy^{2}z^{2}+10x^{3}yz^{3}}{2xyz} =\ ?$

Possible Answers:

$xy - yz+5xz^{2}$

$xy^{2}-3yz+5x^{2}z^{2}$

$xy^{2}-3xz+5xy$

$x^{2}y - 3xyz + 5x^{2}yz^{2}$

$xyz-3yz+5x^{2}yz^{2}$

Correct answer:

$xy^{2}-3yz+5x^{2}z^{2}$

Explanation:

For any polynomial division, divide each term in the numerator individually by the denominator:

$\frac{2x^{2}y^{3}z - 6xy^{2}z^{2}+10x^{3}yz^{3}}{2xyz} =$ $\frac{2x^{2}y^{3}z}{2xyz} - \frac{6xy^{2}z^{2}}{2xyz} + \frac{10x^{3}yz^{3}}{2xyz}=$

$xy^{2}-3yz+5x^{2}z^{2}$

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Example Question #4 : How To Divide Monomial Quotients

Simplify:

$\frac{14x^2y}{7x}$

Possible Answers:

$\frac{1}{2xy}$

98x^3y

98xy

2xy

Correct answer:

2xy

Explanation:

When dividing monomials, consider the coefficients and variables separately. Rewrite the expression as $\left(\frac{14}{7}\right)\left(\frac{x^2}{x}\right)\left(y\right)$ , grouping common bases. For the coeffiecients, we can divide normally: $\left(\frac{14}{7} \right )=2$ . For the variables, we can keep the common base and subtract the exponents: $\left(\frac{x^2}{x} \right )=x^{2-1}=x$ . Then, multiply each portion all back together to obtain 2xy .

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Example Question #1 : Simplifying Expressions

Simplify the expression.

$\small \frac{(x^2y^2)(x^3y^4z)}{x^4y^3z^4}$

Possible Answers:

$\small \frac{x^2y^5}{z^3}$

$\small \frac{xy^3}{z^3}$

$\small \frac{z^3}{x^2y^5}$

$\small \frac{z^3}{xy^3}$

Correct answer:

$\small \frac{xy^3}{z^3}$

Explanation:

$\small \frac{(x^2y^2)(x^3y^4z)}{x^4y^3z^4}$

Because we are only multiplying terms in the numerator, we can disregard the parentheses.

$\small \frac{(x^2y^2)(x^3y^4z)}{x^4y^3z^4}=\frac{x^2y^2x^3y^4z}{x^4y^3z^4}$

To combine like terms in the numerator, we add their exponents.

$\small \frac{x^5y^6z}{x^4y^3z^4}$

To combine like terms between the numerator and denominator, subtract the denominator exponent from the numerator exponent.

$x^{5-4}y^{6-3}z^{1-4}=xy^3z^{-3}$

Remember that any negative exponents stay in the denominator.

$\frac{xy^3}{z^3}$

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Algebra 1 : Monomials

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #461 : Variables

Example Question #42 : How To Multiply A Monomial By A Polynomial

Example Question #43 : How To Multiply A Monomial By A Polynomial

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

Example Question #1 : How To Divide Monomial Quotients

Example Question #2 : How To Divide Monomial Quotients

Example Question #1 : How To Divide Monomial Quotients

Example Question #1 : How To Divide Monomial Quotients

Example Question #4 : How To Divide Monomial Quotients

Example Question #1 : Simplifying Expressions

All Algebra 1 Resources

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