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Algebra II : Basic Single-Variable Algebra

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Example Questions

Example Question #2 : How To Multiply Trinomials

Evaluate the following:

(2x^2-4x+7)(x^2+3x-8)

Possible Answers:

2x^4+2x^3-21x^2+53x-56

2x^4+10x^3-21x^2+53x-56

x^4+2x^3-21x^2+53x-56

2x^4+10x^3+3x^2+53x-56

Correct answer:

2x^4+2x^3-21x^2+53x-56

Explanation:

When multiplying these two trinomials, you'll need to use a modified form of FOIL, by which every term in the first trinomial gets multiplied by every term in the second trinomial. One way to do this is to use the grid method.

You can also solve it piece by piece the way it is set up. First, multiply each of the three terms in the first trinomail by x^2 . Second, multiply each of those three terms again, this time by . Finally multiply the three terms again by .

$(2x^2-4x+7) \times x^2 = 2x^4 - 4x^3 + 7x^2$

$(2x^2-4x+7) \times 3x = 6x^3 - 12x^2 + 21x$

$(2x^2-4x+7) \times -8 = -16x^2 + 32x - 56$

Finally, you can combine like terms after this multiplication to get your final simplified answer:

2x^4+2x^3-21x^2+53x-56

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Example Question #54 : Distributive Property

Evaluate the following to its simplest form:

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

Possible Answers:

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

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

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

None of the available answers

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

Correct answer:

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

Explanation:

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

First we will foil the first function before distributing.

$\frac{1}{2}(4x^2-8x+2x-4)+\frac{1}{3}(2x-3)$

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

We will then distribute out the $\frac{1}{2}$

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

We will then distribute out the $\frac{1}{3}$

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

Now the only like terms we have are $-3x+\frac{2}{3}x$ and -2-1 , so our final answer is:

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

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Example Question #121 : Basic Single Variable Algebra

Simplify the expression: 6(4k+8s)

Possible Answers:

32ks

10k+14s

72ks

24k+48s

24k+8s

Correct answer:

24k+48s

Explanation:

distributes to , multiplying to become 24k , and distributes to , multiplying to make 48s .

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Example Question #123 : Basic Single Variable Algebra

Divide the fractions.

$\frac{30xy}{11} \div \frac{25x^{3}}{22y}$

Possible Answers:

$\frac{12y^{2}}{5x^{2}}$

$\frac{5x^{4}}{12}$

$\frac{5y^{2}}{12x^{2}}$

$\frac{5x^{2}}{12y^{2}}$

$\frac{12x^{4}}{5}$

Correct answer:

$\frac{12y^{2}}{5x^{2}}$

Explanation:

$\frac{30xy}{11} \div \frac{25x^{3}}{22y}$

Dividing fractions is equal to multiplying by the reciprocal.

$\frac{30xy}{11} * \frac{22y}{25x^{3}}$

Cross-cancel the 30 with the 25, and the 22 with the 11.

$\frac{6xy}{1} *\frac{2y}{5x^{3}}$

Combine via multiplication and simplify.

$\frac{6xy* 2y}{5x^{3}}=\frac{6* 2*x* y*y}{5x^{3}}=\frac{12y^{2}}{5x^{2}}$

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Example Question #122 : Basic Single Variable Algebra

Simplify the following expression.

$4x(3x^{2}+x+10)$

Possible Answers:

$11x^{2}+40x$

$12x^{2}+14x$

None of the other answers

$7x^{3}+4x^{2}+14x$

Correct answer:

Explanation:

Distribute the outside term into the parentheses.

$4x(3x^{2}+x+10)=(4x*3x^{2})+(4x *x) +(4x* 10)$

Simplify each distributed factor into one expression.

$12x^{3}+4x^{2}+40x$

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Example Question #81 : Expressions

Simplify the following expression.

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

Possible Answers:

None of the other answers.

$15y^{3}+35y$

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

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

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 #1964 : Algebra Ii

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 #82 : Expressions

Subtract:

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

Possible Answers:

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

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

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

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

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

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 #83 : Expressions

Subtract:

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

Possible Answers:

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

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

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

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

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

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 #84 : Expressions

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

Possible Answers:

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

$x^{3} -125$

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

$x^{3} +125$

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

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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Algebra II : Basic Single-Variable Algebra

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #2 : How To Multiply Trinomials

Example Question #54 : Distributive Property

Example Question #121 : Basic Single Variable Algebra

Example Question #123 : Basic Single Variable Algebra

Example Question #122 : Basic Single Variable Algebra

Example Question #81 : Expressions

Example Question #1964 : Algebra Ii

Example Question #82 : Expressions

Example Question #83 : Expressions

Example Question #84 : Expressions

All Algebra II Resources

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