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Algebra 1 : Variables

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #35 : Monomials

Multiply: 2xy^3(x^2+y^3-xy)

Possible Answers:

2x^2y^3+2xy^6-2x^2y^3

$\frac{2y^3}{x}+2xy^6-2y^2$

2x^3y^3+y^3-xy

2x^3y^3+2xy^6-2x^2y^4

2x^4y^7

Correct answer:

2x^3y^3+2xy^6-2x^2y^4

Explanation:

Distribute the monomial throughout the terms of the polynomial.

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

Simplify these terms. When similar bases of a particular power are multiplied, their powers can be added.

The answer is: 2x^3y^3+2xy^6-2x^2y^4

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Example Question #36 : How To Multiply A Monomial By A Polynomial

Multiply with 3x^2+3x+6 .

Possible Answers:

5x^2+3x+6

12x^3+12x

5x^3+5x^2+8x

6x^3+6x^2+12x

6x^2+3x+6

Correct answer:

6x^3+6x^2+12x

Explanation:

Write the expression of the multiplied terms.

2x(3x^2+3x+6)

Distribute the monomial with each term in the polynomial.

2x(3x^2)+2x(3x)+2x(6)

Simplify this expression.

The answer is: 6x^3+6x^2+12x

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Example Question #37 : How To Multiply A Monomial By A Polynomial

Multiply: -3y^2(x-y-y^2+z)

Possible Answers:

-3xy^2-3y^3-3y^4+3y^2z

-3xy^2+6y^4-3y^2z

-3xy^2+3y^3+3y^4-3y^2z

-3xy^4z

-3xy^2+3y^2+3y^3-3y^2z

Correct answer:

-3xy^2+3y^3+3y^4-3y^2z

Explanation:

Distribute the monomial throughout each term in the polynomial. Be careful with sign changes.

(-3y^2)(x)-(-3y^2)(y)-(-3y^2)(y^2)+(-3y^2)(z)

Simplify each term. The powers of similar bases multiplied by each other can be added.

-3xy^2+3y^3+3y^4-3y^2z

There are no like terms.

The answer is: -3xy^2+3y^3+3y^4-3y^2z

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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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Algebra 1 : Variables

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #35 : Monomials

Example Question #36 : How To Multiply A Monomial By A Polynomial

Example Question #37 : How To Multiply A Monomial By A Polynomial

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

All Algebra 1 Resources

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