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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #34 : Monomials

Multiply: 3x^4(x^2+x-6)

Possible Answers:

$3x^{8}+3x^{4}-18x^4$

$4x^{8}+4x^{4}-9x^4$

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

$4x^{6}+4x^{5}-9x^4$

$3x^{6}+3x^{5}-18x^4$

Correct answer:

$3x^{6}+3x^{5}-18x^4$

Explanation:

Multiply by distributing the 3x^4 term across each term in the parentheses.

3x^4(x^2+x-6) = (3x^4)(x^2)+(3x^4)(x)+(3x^4)(-6)

Expand each term. When multiplying similar bases with a power, their powers can be added.

$3x^{4+2}+3x^{4+1}-18x^4$

Simplify.

The answer is: $3x^{6}+3x^{5}-18x^4$

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Example Question #4692 : Algebra 1

Multiply: 3x^2(-x^2+3x-6)

Possible Answers:

2x^2+9x-18

-3x^2+9x-18

-3x^4+9x^3-18x^2

2x^2+3x-6

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

Correct answer:

-3x^4+9x^3-18x^2

Explanation:

To simplify this expression, simply distribute the monomial throughout the terms inside the polynomial.

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

Simplify all the terms. When multiplying bases with a power, it is the same as adding the powers.

The answer is: -3x^4+9x^3-18x^2

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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:

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

$-1+7w^{2}$

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

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

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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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #34 : Monomials

Example Question #4692 : Algebra 1

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

All Algebra 1 Resources

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