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Algebra II : Algebra II

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Example Questions

Example Question #4263 : Algebra 1

Evaluate the following:

$\frac{1}{2}(6x^2+2x-3) + \frac{1}{4}(12x^2-24x+6)$

Possible Answers:

6x^2-7x

6x^2+5x + 3

6x^2-5x

$6x^2-5x + \frac{3}{2}$

Correct answer:

6x^2-5x

Explanation:

With this problem, you need to distribute the two fractions across each of the trinomials. To do this, you multiply each term inside the parentheses by the fraction outside of it:

$\frac{1}{2}(6x^2+2x-3) + \frac{1}{4}(12x^2-24x+6)$

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

The next step is to combine like terms, based on the variables. You have two terms with x^2 , two terms with , and two terms with no variable. Make sure to pay attention to plus and minus signs with each term when combining like terms. Since you have a positive and negative $\frac{3}{2}$ , those two terms will cancel out:

6x^2-5x

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Example Question #2 : How To Multiply Trinomials

Evaluate the following:

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

Possible Answers:

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

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

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

x^4+2x^3-21x^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 #55 : How To Use Foil In The Distributive Property

Evaluate the following to its simplest form:

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

Possible Answers:

None of the available answers

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

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

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

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

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 #1961 : Algebra Ii

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

Possible Answers:

24k+48s

32ks

72ks

10k+14s

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 #1962 : Algebra Ii

Simplify the following expression.

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

Possible Answers:

$12x^{2}+14x$

None of the other answers

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

$11x^{2}+40x$

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 #1963 : Algebra Ii

Simplify the following expression.

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

Possible Answers:

$15y^{3}+35y$

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

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

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 #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 #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:

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

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

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

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

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

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 #1964 : Algebra Ii

Subtract:

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

Possible Answers:

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

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

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

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

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

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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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #4263 : Algebra 1

Example Question #2 : How To Multiply Trinomials

Example Question #55 : How To Use Foil In The Distributive Property

Example Question #1961 : Algebra Ii

Example Question #123 : Basic Single Variable Algebra

Example Question #1962 : Algebra Ii

Example Question #1963 : Algebra Ii

Example Question #1964 : Algebra Ii

Example Question #5 : How To Subtract Polynomials

Example Question #1964 : Algebra Ii

All Algebra II Resources

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