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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 #21 : Intermediate Single Variable Algebra

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

Possible Answers:

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

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

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

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

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

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 #4672 : Algebra 1

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

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

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Example Question #18 : Monomials

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

Possible Answers:

7x^5 -2x^2

-3x^2

12x^5 - 15x^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 #14 : Monomials

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

Possible Answers:

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

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

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

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

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

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 #441 : Variables

Multiply: xy(x^2+x)

Possible Answers:

3xy+2x

x^3y+x^2y

2x^2y+2xy

2x^2+3x+y

2x^2y+2xy

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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Example Question #442 : Variables

Simplify:

$5 \times 10xy$

Possible Answers:

5xy

50xy

The answers provided do not show the correct simplificaiton.

$50x \times 50y$

$15x \times y$

Correct answer:

50xy

Explanation:

When multiplying a whole number by a polynomial, we simply multiply that number by whatever coefficient is present in front of the variables of the polynomial. We then maintain the variables in the simplified expression.

$10 \times 5 = 50$

50xy

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Example Question #22 : Monomials

Simplify the following expression:

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

Possible Answers:

$6x^{2}y+9y^{2}-21xy$

$6x^{3}y^{2}+9xy^{3}-21xy$

$5x^{2}y+6xy^{2}-10xy$

$6x^{2}y+9xy^{2}-21xy$

$\frac{2}{3}x+y-\frac{7}{3}xy$

Correct answer:

$6x^{3}y^{2}+9xy^{3}-21xy$

Explanation:

Use the distributive property to multiply the monomial and polynomial.

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

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

$6x^{3}y^{2}+9xy^{3}-21xy$

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Example Question #23 : Monomials

Evaluate the expression:

$5x(x^{2}-3x+1)$

Possible Answers:

$-10x^{2}+5x$

$5x^{3}+15x^{2}+5x$

$5x^{3}-15x^{2}+5x$

$x^{2}+2x+1$

$5x^{3}-3x+1$

Correct answer:

$5x^{3}-15x^{2}+5x$

Explanation:

Multipying a monomial and trinomial boils down to distributing the monomial amongst all the parts of the trinomial as such:

$5x(x^{2}-3x+1)=(5x\cdotx^{2})+(5x\cdot-3x)+(5x\cdot1)$

After some cleanup we get:

$5x^{3}-15x^{2}+5x$

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Example Question #443 : Variables

Multiply: $4r(3r^{2}+2r-12)$

Possible Answers:

$12r^{3}+20r^{2}-48r$

$12r^{3}-40r$

$20r^{2}-48r$

$4r^{3}+8r^{2}-48r$

$12r^{3}+8r^{2}-48r$

Correct answer:

$12r^{3}+8r^{2}-48r$

Explanation:

$4r(3r^{2}+2r-12)$

All we need to do here is multiply every term within the polynomial $(3r^{2}+2r-12)$ by the monomial on the outside of the parentheses: .

To do this we need to multiply every term by and by . Remember that when we multiply by a variable (in this case ), we need to add to each of the exponents.

So this leaves us with $12r^{3}+8r^{2}-48r$ .

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Example Question #4673 : Algebra 1

Divide: $\frac{x^2+x}{2x^2-2x}$

Possible Answers:

$-\frac{1}{2}$

$\frac{1}{x-1}$

$\frac{x+1}{2x-2}$

$\textup{The fraction is already simplified to its fullest.}$

Correct answer:

$\frac{x+1}{2x-2}$

Explanation:

To divide this, we must pull out a common factor from the numerator and denominator.

The common factor from the numerator is only .

The common factor from the denominator is .

$\frac{x^2+x}{2x^2-2x} = \frac{x\cdot(x+1)}{2\cdot x\cdot (x-1)}$

The only term that will cancel is the . We cannot cancel the inside x+1 and x-1 terms because they are different entities of a quantity.

$\frac{x\cdot(x+1)}{2\cdot x\cdot (x-1)} = \frac{x+1}{2(x-1)} = \frac{x+1}{2x-2}$

The answer is: $\frac{x+1}{2x-2}$

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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #21 : Intermediate Single Variable Algebra

Example Question #4672 : Algebra 1

Example Question #18 : Monomials

Example Question #14 : Monomials

Example Question #441 : Variables

Example Question #442 : Variables

Example Question #22 : Monomials

Example Question #23 : Monomials

Example Question #443 : Variables

Example Question #4673 : Algebra 1

All Algebra 1 Resources

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