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Algebra II : Expressions

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Example Questions

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Example Question #32 : Simplifying Expressions

Simplify the following expression.

$5y(3y^{3}-2y+9)$

Possible Answers:

$8y^{4}+3y^{2}+14y$

$15y^{3}+35y$

$8y^{4}-7y^{2}+14y$

None of the other answers.

Correct answer:

Explanation:

Distribute the outside term into the parentheses.

$5y(3y^{3}-2y+9)=(5y* 3y^{3})- (5y* 2y) + (5y*9)$

Simplify each distributed factor into one expression.

$15y^{4}-10y^{2}+45y$

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Example Question #123 : Monomials

Multiply. Give the answer in simplest form.

$\left(\frac{3}{2x^2} \right )\cdot\left(\frac{4x^2y}{9} \right )$

Possible Answers:

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

$\frac{12y}{9}$

$\frac{2y}{3}$

2x^4y

Correct answer:

$\frac{2y}{3}$

Explanation:

Multiplying quotients is similar to multiplying fractions, so we multiply straight across to get $\small \frac{12x^2y}{18x^2}$ . From this point, we can simplify. Since $\small \frac{12}{18}=\frac{2}{3}$ and $\small \frac{x^2}{x^2}=x^{2-2}=x^0=1$ , our final answer becomes $\small \frac{2}{3} \cdot 1 \cdot y = \frac{2y}{3}$ .

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Example Question #5 : How To Subtract Polynomials

Subtract:

$\left (\frac{1}{2}x + \frac{2}{3} \right ) - \left (\frac{1}{4}x - \frac{1}{6} \right )$

Possible Answers:

$-\frac{1}{4}x + \frac{5}{6}$

$\frac{1}{4}x + \frac{5}{6}$

$\frac{1}{4}x + \frac{1}{2}$

$\frac{1}{4}x + \frac{1}{9}$

$-\frac{1}{4}x + \frac{1}{2}$

Correct answer:

$\frac{1}{4}x + \frac{5}{6}$

Explanation:

$\left (\frac{1}{2}x + \frac{2}{3} \right ) - \left (\frac{1}{4}x - \frac{1}{6} \right )$

$=\frac{1}{2}x + \frac{2}{3} - \frac{1}{4}x + \frac{1}{6}$

$=\frac{1}{2}x - \frac{1}{4}x + \frac{2}{3} + \frac{1}{6}$

$=\frac{2}{4}x - \frac{1}{4}x + \frac{4}{6} + \frac{1}{6}$

$=\frac{1}{4}x + \frac{5}{6}$

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Example Question #6 : How To Subtract Polynomials

Subtract:

$(7.5x^{2} + 2.4x - 4.6) - (x^{2} - 3.2x - 1.5)$

Possible Answers:

$7.5x^{2} + 5.6x - 3.1$

$6.5x^{2} -0.8x - 6.1$

$6.5x^{2} + 5.6x - 3.1$

$6.5x^{2} -0.8x - 3.1$

$6.5x^{2} + 5.6x - 6.1$

Correct answer:

$6.5x^{2} + 5.6x - 3.1$

Explanation:

$(7.5x^{2} + 2.4x - 4.6) - (x^{2} - 3.2x - 1.5)$

$= 7.5x^{2} + 2.4x - 4.6 - x^{2} + 3.2x +1.5$

$= 7.5x^{2} - 1x^{2} + 2.4x + 3.2x - 4.6 +1.5$

$= 6.5x^{2} + 5.6x - 3.1$

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Example Question #82 : Expressions

Multiply: $(x -5) (x^{2} +5x + 25)$

Possible Answers:

$x^{3} -20x +125$

$x^{3} -125$

$x^{3} +125$

$x^{3} -20x -125$

$x^{3} -20x^{2} -125$

Correct answer:

$x^{3} -125$

Explanation:

$(x -5) (x^{2} +5x + 16)$

$= x (x^{2} +5x + 25)-5 (x^{2} +5x + 25)$

$= x \cdot x^{2} +x \cdot 5x + x \cdot 25-5 \cdot x^{2} -5 \cdot 5x -5 \cdot 25$

$= x^{3} +5x^{2} +25x-5 x^{2} -25x -125$

$= x^{3} +5x^{2} -5 x^{2} +25x -25x -125$

$= x^{3} -125$

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Example Question #10 : How To Add Trinomials

Add:

(3x^2+14x+9) +(x^2-2x+4)

Possible Answers:

-8x+13

2x^2+16x+5

4x^2+12x+13

4x^4-12x^2+13

3x^4+12x^2+36

Correct answer:

4x^2+12x+13

Explanation:

To add trinomials, identify and group together the like-terms: (3x^2+x^2) +(14x-2x)+(9+4) . Next, factor out what is common between the like-terms: (3+1)x^2+(14-2)x+(9+4) . Finally, add what is left inside the parentheses to obtain the final answer of 4x^2+12x+13 .

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Example Question #125 : Monomials

Simplify:

$\frac{c^{4}}{4}*\frac{3a^{2}}{b^{2}}$

Possible Answers:

$\frac{4a^{2}b^{2}c^{4}}{3}$

$\frac{4b^{2}}{3a^{2}c^{4}}$

$\frac{3}{4}a^{2}b^{2}c^{4}$

$\frac{3a^{2}b^{2}c^{4}}{4}$

$\frac{3a^{2}c^{4}}{4b^{2}}$

Correct answer:

$\frac{3a^{2}c^{4}}{4b^{2}}$

Explanation:

Since there are no like terms in the numerator or in the denominator, you can only combine ther terms on the numerator and denominator so that they are in one quotient. You cannot further combine the variables because each variable is represented by a different letter. You cannot further reduce the integers because they do not have a common factor.

$\frac{c^{4}}{4}*\frac{3a^{2}}{b^{2}}=\frac{3a^{2}c^{4}}{4b^{2}}$

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Example Question #41 : Simplifying Expressions

Simplify the expression.

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

Possible Answers:

4x+2

-x-2

4x-2

-x+2

Correct answer:

4x-2

Explanation:

First, rearrange the order of the problem by grouping like terms together:

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

Now, combine the like terms:

3x-x+2x-2=2x+2x+2=4x+2.

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Example Question #42 : Simplifying Expressions

Simplify the following expression:

$4x^{2} + 3x - 12y^{2} + x^{2} - 20y + 5y - 12y^{2}$

Possible Answers:

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

$8x^{2} - 44y^{2}$

$5x^{2} -24y^{2} + 3x - 15y$

None of the other answers

$-20x^{2} - 12x$

Correct answer:

$5x^{2} -24y^{2} + 3x - 15y$

Explanation:

To simplify an expression you need to combine like terms.

So,

$4x^{2} + x^{2} = 5x^{2}$

$-12y^{2} - 12y^{2} = -24y^{2}$

-20y + 5y = -15y

and cannot be combined with anything.

To then rewrite the expression you want to work in alphabetical order, and in decreasing exponential power.

$5x^{2} -24y^{2} + 3x - 15y$

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Example Question #43 : Simplifying Expressions

Simplify: $\frac{2x^2y^5}{3xy^5}\cdot \frac{x^4y}{x^3y^5}$

Possible Answers:

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

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

The answer is not present.

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

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

Correct answer:

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

Explanation:

$\frac{2x^2y^5}{3xy^5}\cdot \frac{x^4y}{x^3y^5}$

This problem is best simplified by dealing with the fractions separately and then combining. The rules of exponents used are: $\frac{a^m}{a^n}=a^{m-n}$ , $a^m*a^n=a^{m*n}$ , a^0=1 , and $a^{-m}=\frac{1}{a^m}$ .

$\frac{2x^2y^5}{3xy^5}\cdot \frac{x^4y}{x^3y^5} \rightarrow \frac{2x}{3}\cdot\frac{xy^{-4}}{1}\rightarrow \frac{2x}{3}\cdot\frac{x}{y^4}\rightarrow \frac{2x^2}{3y^4}$

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Algebra II : Expressions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #32 : Simplifying Expressions

Example Question #123 : Monomials

Example Question #5 : How To Subtract Polynomials

Example Question #6 : How To Subtract Polynomials

Example Question #82 : Expressions

Example Question #10 : How To Add Trinomials

Example Question #125 : Monomials

Example Question #41 : Simplifying Expressions

Example Question #42 : Simplifying Expressions

Example Question #43 : Simplifying Expressions

All Algebra II Resources

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