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Algebra 1 : Algebra 1

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Example Questions

Example Question #153 : Monomials

Simplify: $\frac {(x^{2}y)^{3}}{ (xy)^{4}}$ .

What is the exponent of in the simplified form, and does it appear in the numerator or denominator?

Possible Answers:

1, in the numerator

1, in the denominator

does not appear in the simplified form of the expression

2, in the denominator

2, in the numerator

Correct answer:

1, in the denominator

Explanation:

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

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

$=\frac {x^{2 \cdot 3 }\cdot y ^{3}}{ x^{4} \cdot y^{4}}$

$=\frac {x^{6 }\cdot y ^{3}}{ x^{4} \cdot y^{4}}$

$=\frac {x^{6-4}}{ y^{4 -3}}$

$=\frac {x^{2}}{ y^{1}}$

The exponent of is 1, in the denominator.

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Example Question #574 : Variables

Simplify: $\frac {(x^{2}y)^{3}}{ (xy)^{4}}$ .

What is the exponent of in the simplified form, and does it appear in the numerator or denominator?

Possible Answers:

1, in the numerator

2, in the numerator

does not appear in the simplified form of the expression

1, in the denominator

2, in the denominator

Correct answer:

2, in the numerator

Explanation:

To simplify this expression use the law of exponents which state that when a term is raised to a power, multiply the exponents. Also, when terms of like bases are divided the exponents are subtracted.

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

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

$=\frac {x^{2 \cdot 3 }\cdot y ^{3}}{ x^{4} \cdot y^{4}}$

$=\frac {x^{6 }\cdot y ^{3}}{ x^{4} \cdot y^{4}}$

$=\frac {x^{6-4}}{ y^{4 -3}}$

$=\frac {x^{2}}{ y^{1}}$

The exponent of is 2, in the numerator.

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Example Question #581 : Variables

Simplify the expression

$\frac{(3x^{4})^{2}}{2x^{3}}$ .

What is the coefficient in this expression after it is simplified?

Possible Answers:

$\frac{9}{2}$

$\frac{9}{4}$

Correct answer:

$\frac{9}{2}$

Explanation:

To simplify the expression use the rule of exponents which states that when like bases are raised to a power the exponents are multiplied together. When like bases are divided that means that their exponents are subtracted.

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

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

$= \frac{9x^{4 \cdot 2}}{2x^{3}}$

$= \frac{9x^{8}}{2x^{3}}$

$= \frac{9}{2} \cdot \frac{x^{8}}{x^{3}}$

$= \frac{9}{2} \cdot x^{8-3}$

$= \frac{9}{2} x^{5}$

The coefficient of this simplified form is $\frac{9}{2}$ .

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Example Question #582 : Variables

Simplify: $\frac{\sqrt{x} \cdot \sqrt[3]{y}}{x^2y^4}$

Possible Answers:

$x^{\frac{3}{2}} y^{\frac{11}{3}}$

$\textup{Cannot be reduced any further.}$

$x^{\frac{2}{3}} y^{\frac{3}{11}}$

$\frac{1}{x^{\frac{3}{2}} y^{\frac{11}{3}}}$

$\frac{1}{x^{\frac{2}{3}} y^{\frac{3}{11}}}$

Correct answer:

$\frac{1}{x^{\frac{3}{2}} y^{\frac{11}{3}}}$

Explanation:

In order to simplify, rewrite the numerator in terms of exponential powers.

$\frac{\sqrt{x} \cdot \sqrt[3]{y}}{x^2y^4} = \frac{x^{\frac{1}{2}} y^{\frac{1}{3}}}{x^2y^4}$

Because similar bases are divided, subtract the powers of the numerator with the denominator.

$x^{\frac{1}{2}-2}= x^{\frac{1}{2}-\frac{4}{2}} = x^{-\frac{3}{2}}$

$y^{\frac{1}{3}-4} = y^{\frac{1}{3}-\frac{12}{3}} =y^{-\frac{11}{3}}$

Since these two variables have negative exponents, we can simply take the inverse of both to eliminate the negative exponents.

$x^{-\frac{3}{2}} = \frac{1}{x^{\frac{3}{2}}}$

$y^{-\frac{11}{3}} = \frac{1}{y^{\frac{11}{3}}}$

Multiply both fractions.

The answer is: $\frac{1}{x^{\frac{3}{2}} y^{\frac{11}{3}}}$

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Example Question #3 : Foil

What is the equation that has the following solutions? x=5,-8

Possible Answers:

$x^{2}+5x-60$

$x^{2}-3x+40$

$x^{2}+13x-40$

$x^{2}+3x-40$

Correct answer:

$x^{2}+3x-40$

Explanation:

This is a FOIL-ing problem. First, set up the numbers in a form we can use to create the function.

Take the opposite sign of each of the numbers and place them in this format. (x-5)(x+8)

Multiply the in the first parentheses by the and 8 in the second parentheses respectively to get $x^{2}+8x$

Multiply the in the first parentheses by the and 8 in the second parentheses as well to give us -5x-40 .

Then add them together to get $x^{2}+8x-5x-40$

Combine like terms to find the answer which is $x^{2}+3x-40$ .

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Example Question #1 : Distributive Property

Simplify the following expression.

$(3x^{2}-3)(2x^{3}-8)$

Possible Answers:

$6x^{5}-30x^{2}+24$

$6x^{5}-6x^{3}-24x^{2}-24$

$6x^{5}-30x^{2}-24$

$6x^{5}-6x^{3}-24x^{2}+24$

$6x^{6}-6x^{3}-24x^{2}+24$

Correct answer:

$6x^{5}-6x^{3}-24x^{2}+24$

Explanation:

Simplify using FOIL method.

Remember that multiplying variables means adding their exponents.

F: $3x^{2}*2x^{3} = 6x^{5}$

O: $3x^{2}*(-8) = -24x^{2}$

I: $-3 *2x^{3}=-6x^{3}$

L: -3 *-8= 24

Combine the terms. Note that we cannot simplify further, as the exponents do not match and cannot be combined.

$6x^{5}-6x^{3}-24x^{2}+24$

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Example Question #1 : How To Use Foil In The Distributive Property

$\left ( 3x+2\right )\left ( 2x-5\right )=$

Possible Answers:

$6x^{2}+19x -10$

$6x^{2}+2x-3$

$6x^{2}-3x-10$

$6x^{2}-11x-10$

$6x^{2}+19x+10$

Correct answer:

$6x^{2}-11x-10$

Explanation:

$\textup{FOIL: Product is the sum of the products of the first, outer, inner and last terms:}$

$\left ( 3x+2\right )\left ( 2x-5\right )=$ $3x\ast2x+3x\left ( -5\right )+ 2\ast2x+2\left ( -5\right )$

$6x^{2}-15x+4x-10\;\;\;=\;\;\;6x^{2}-11x-10$

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Example Question #2 : How To Use Foil In The Distributive Property

What are the factors of $x^{2}+11x+24$ ?

Possible Answers:

(x+8)(x+3)

(x+6)(x+4)

(x+8)(x+4)

(x+11)(x+13)

(x+10)(x+1)

Correct answer:

(x+8)(x+3)

Explanation:

To find the factors, you must determine which of the sets of factors result in the polynomial when multiplied together. Using the FOIL method, a set of factors with the form (x+a)(x+b) will result in $x^{2}+ax+bx+ab$ . Applying this format to the given equation of $x^{2}+11x+24$ , a+b must equal 11 and must equal 24. The only set that works is (x+8)(x+3) .

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Example Question #3 : How To Use Foil In The Distributive Property

Expand:

(x+3)(2x-5)

Possible Answers:

$2x^{2}-2x-15$

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

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

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

$x^{2}-2x-15$

Correct answer:

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

Explanation:

If you use the FOIL method, you will multiply each expression individually. So, (x+3)(2x-5) becomes (x*2x)+(x*-5)+(3*2x)+(3*-5) , which simplifies to $2x^{2}+x-15$ .

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Example Question #1 : How To Use Foil In The Distributive Property

Simplify the expression below.

$x^{2}y(2x + 3y)$

Possible Answers:

$5x^{2}y + 6x^{2}y^{2}$

$3x^{2}y + 4xy^{2}$

$2x^{3}y + 3x^{2}y^{2}$

$2x^{2}y + 3xy^{2}$

$4x^{3}y + 5x^{2}y^{2}$

Correct answer:

$2x^{3}y + 3x^{2}y^{2}$

Explanation:

$x^{2}y(2x + 3y)$

Use the distributive property to simplify the expression. In general, a(b+c) = ab + ac .

$x^{2}y(2x + 3y)=(x^{2}y*2x) + (x^{2}y*3y)$

Now we can begin to combine like terms through multiplication.

$(x^{2}y*2x) + (x^{2}y*3y)$

$(2x^{3}y)+(3x^2y^2)$

We cannot simplify further.

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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #153 : Monomials

Example Question #574 : Variables

Example Question #581 : Variables

Example Question #582 : Variables

Example Question #3 : Foil

Example Question #1 : Distributive Property

Example Question #1 : How To Use Foil In The Distributive Property

Example Question #2 : How To Use Foil In The Distributive Property

Example Question #3 : How To Use Foil In The Distributive Property

Example Question #1 : How To Use Foil In The Distributive Property

All Algebra 1 Resources

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