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Algebra II : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #2 : Simplifying And Expanding Quadratics

Multiply: $(x + 4) (x^{2} -4x + 16)$

Possible Answers:

$x^{3}- 12x - 64$

$x^{3}- 20x + 64$

$x^{3}- 12x + 64$

$x^{3} - 64$

$x^{3} + 64$

Correct answer:

$x^{3} + 64$

Explanation:

$(x + 4) (x^{2} -4x + 16)$

$= x (x^{2} -4x + 16)+ 4 (x^{2} -4x + 16)$

$= x \cdot x^{2} -x \cdot 4x + x \cdot 16+ 4 \cdot x^{2} -4 \cdot 4x + 4 \cdot 16$

$= x^{3} -4x^{2} + 16x+ 4 x^{2} -16x + 64$

$= x^{3} -4x^{2} + 4 x^{2} + 16x -16x + 64$

$= x^{3} + 64$

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Example Question #4281 : Algebra 1

Subtract:

(x^2+15x-3)-(x^2-5x-3)

Possible Answers:

20x^2

2x^2+20x+6

20x+6

20x

x^4+20x^2+6

Correct answer:

20x

Explanation:

When subtracting trinomials, first distribute the negative sign to the expression being subtracted, and then remove the parentheses: (x^2+15x-3)-(x^2-5x-3)=x^2+15x-3-x^2+5x+3

Next, identify and group the like terms in order to combine them: (x^2-x^2)+(15x+5x)+(3-3)=20x .

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Example Question #2 : How To Multiply Trinomials

Evaluate the following:

(x^2+2x-4)(2x+5)

Possible Answers:

2x^3+9x^2+18x-20

4x^3+6x^2+2x-20

2x^3+9x^2+2x-20

2x^3+9x^2+2x+20

Correct answer:

2x^3+9x^2+2x-20

Explanation:

When multiplying this trinomial by this binomial, you'll need to use a modified form of FOIL, by which every term in the binomial gets multiplied by every term in the 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 trinomail by . Then multiply each of those three terms again, this time by .

$(x^2+2x-4) \times 2x = 2x^3 + 4x^2 - 8x$

$(x^2+2x-4) \times 5 = 5x^2 + 10x - 20$

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

2x^3 + 9x^2 +2x-20

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Example Question #11 : Simplifying And Expanding Quadratics

Expand:

(x-9)(3x+2)

Possible Answers:

None of the other answers

$3x^{2}-25x-18$

$3x^{2}-29x-18$

$3x^{2}-18x-29$

$3x^{2}-18x-25$

Correct answer:

$3x^{2}-25x-18$

Explanation:

To multiple these binomials, you can use the FOIL method to multiply each of the expressions individually.This will give you

(x)(3x)+(x)(2)+(-9)(3x)+(-9)(2)

or $3x^{2}-25x-18$ .

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Example Question #3 : How To Add Trinomials

Evaluate the following:

$\left(\frac{1}{2}x^2 +2x - 4\right) + \left(\frac{3}{2}x^2 -5x -4\right)$

Possible Answers:

x^2+3x-8

2x^2-3x

2x^2-3x-8

2x^2+3x+8

Correct answer:

2x^2-3x-8

Explanation:

To add these two trinomials, you will first begin by combining like terms. You have two terms with x^2 , two terms with , and two terms with no variable. For the two fractions with x^2 , you can immediately add because they have common denominators:

$(\frac{1}{2}x^2 +2x - 4) + (\frac{3}{2}x^2 -5x -4)$

$\frac{4}{2}x^2 -3x - 8$

2x^2 -3x - 8

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Example Question #11 : Quadratic Equations And Inequalities

Simplify.

$\small \small \frac{x^2+5x+6}{x^3+2x^2-16x-32}$

Possible Answers:

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

$\small \small \frac{x+3}{(x+4)(x+4)}$

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

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

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

Correct answer:

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

Explanation:

Factoring the expression gives $\small \frac{}{}$ $\small \small \frac{(x+3)(x+2)}{(x-4)(x+4)(x+2)}$ . Values that are in both the numerator and denominator can be cancelled. By cancelling $\small x+2$ , the expression becomes $\small \small \frac{(x+3)}{(x-4)(x+4)}$ .

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Example Question #11 : Quadratic Equations And Inequalities

Simplfy.

$\small \frac{x^2-2x-15}{x^2-3x-10}$

Possible Answers:

$\small \small \frac{x+2}{x+3}$

$\small \small \frac{x+3}{x-2}$

$\small \small \frac{x-3}{x+2}$

$\small \frac{x+3}{x+2}$

$\small \small \small \frac{x-2}{x+3}$

Correct answer:

$\small \frac{x+3}{x+2}$

Explanation:

By factoring the equation you get $\small \small \small \frac{(x+3)(x-5)}{(x+2)(x-5)}$ . Values that are in both the numerator and denominator can be cancelled. Cancelling the $\small x-5$ values gives $\small \small \small \frac{x+3}{x+2}$ .

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Example Question #13 : Quadratic Equations And Inequalities

Expand.

$\small 2(x+2)(x+4)$

Possible Answers:

$\small x^2+4x+8$

$\small \small 2x^2+12x-16$

$\small 2x+12x+16$

$\small 2x^2+12x+16$

$\small \small x^2+4x-8$

Correct answer:

$\small 2x^2+12x+16$

Explanation:

By foiling the binomials, multiplying the firsts, then the outers, followed by the inners and lastly the lasts, the expression you get is:

$\small 2(x^2+4x+2x+8)$ .

However, the expression can not be considered simplified in this state.

Distributing the two and adding like terms gives $\small 2x^2+12x+16$ .

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Example Question #12 : Understanding Quadratic Equations

If (ax+b)(2ax+3b)=8x^2+30x+27 , what is the value of a-b ?

Possible Answers:

Correct answer:

Explanation:

Use the FOIL method to simplify the binomial.

(a+b)(c+d) = ac+ad+bc+bd

(ax)(2ax)+(ax)(3b)+(b)(2ax)+(b)(3b)

Simplify the terms.

2a^2x^2+5abx+3b^2=8x^2+30x+27

Notice that the coefficients can be aligned to the unknown variables. Solve for and .

$2a^2 = 8 \rightarrow a^2 = 4 \rightarrow a=2$

$3b^2 = 27\rightarrow b^2=9 \rightarrow b=3$

a-b = 2-3 = -1

The answer is:

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Example Question #171 : Intermediate Single Variable Algebra

Multiply: (x^2-x-1)(3x^2-x+3)

Possible Answers:

$\textup{The answer is not given.}$

3x^4-3x^3-x^2-2x-3

3x^4-3x^3-x^2+2x-3

3x^4-4x^3+x^2-2x-3

3x^4-4x^3+4x^2-4x-3

Correct answer:

3x^4-4x^3+x^2-2x-3

Explanation:

Multiply each term of the first trinomial by second trinomial.

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

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

(-1)(3x^2-x+3) = -3x^2+x-3

Add and combine like-terms.

The answer is: 3x^4-4x^3+x^2-2x-3

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Algebra II : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #2 : Simplifying And Expanding Quadratics

Example Question #4281 : Algebra 1

Example Question #2 : How To Multiply Trinomials

Example Question #11 : Simplifying And Expanding Quadratics

Example Question #3 : How To Add Trinomials

Example Question #11 : Quadratic Equations And Inequalities

Example Question #11 : Quadratic Equations And Inequalities

Example Question #13 : Quadratic Equations And Inequalities

Example Question #12 : Understanding Quadratic Equations

Example Question #171 : Intermediate Single Variable Algebra

All Algebra II Resources

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