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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 #59 : Foil

Solve: (3x-3)(9-2x)

Possible Answers:

6x^2-33x-27

-6x^2-21x-27

-6x^2-33x-27

-6x^2+21x-27

-6x^2+33x-27

Correct answer:

-6x^2+33x-27

Explanation:

Simplify the terms by using the FOIL method.

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

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

Simplify the terms in parentheses.

27x-6x^2-27+6x

Combine like terms and reorder the terms from highest to lowest order.

The answer is: -6x^2+33x-27

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Example Question #60 : Foil

Evaluate: $(\sqrt{3}+\sqrt{8})(\sqrt{3}-\sqrt2)$

Possible Answers:

$\sqrt{6}-1$

$3\sqrt{2}-7$

$2\sqrt{3}-1$

$\sqrt{6}-1$

$7-2\sqrt6$

Correct answer:

$\sqrt{6}-1$

Explanation:

Evaluate this by using the FOIL method.

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

Use this equation to determine the value of the problem.

$(\sqrt{3}+\sqrt{8})(\sqrt{3}-\sqrt2)$

$(\sqrt3)(\sqrt3)+(\sqrt3)(-\sqrt2)+(\sqrt8)(\sqrt3)+(\sqrt8)(-\sqrt2)$

Simplify the expression.

$3-\sqrt6+\sqrt{24}-\sqrt{16}$

Simplify all radicals, if possible.

$3-\sqrt6+2\sqrt{6}-4 = \sqrt{6}-1$

The answer is: $\sqrt{6}-1$

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Example Question #61 : Foil

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

Possible Answers:

$\frac{1}{3}x^2-2x+12$

$\frac{1}{3}x^2-4x+12$

$\frac{1}{3}x^2+12$

$\frac{1}{3}x^2-12$

$\frac{1}{3}x^2-x+12$

Correct answer:

$\frac{1}{3}x^2-12$

Explanation:

Solve by using the FOIL method.

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

Simplify the expression given.

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

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

Simplify the terms. To multiply a fraction with another number, multiply the numerator with the whole number.

$\frac{1}{3}x^2+2x-2x-12 = \frac{1}{3}x^2-12$

The answer is: $\frac{1}{3}x^2-12$

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Example Question #81 : Quadratic Equations And Inequalities

Solve: (3x-10)(x-7)

Possible Answers:

3x^2-31x+70

3x^2+9x+70

3x^2+31x+70

3x^2-9x+70

3x^2-11x+70

Correct answer:

3x^2-31x+70

Explanation:

Solve by using the FOIL method.

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

Simplify the question by using this format.

(3x-10)(x-7)

(3x)(x)+(3x)(-7)+(-10)(x)+(-10)(-7)

Simplify the terms.

3x^2-21x-10x+70 = 3x^2-31x+70

The answer is: 3x^2-31x+70

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Example Question #82 : Understanding Quadratic Equations

Simplify: $(\sqrt{2}-2)(\sqrt{8}+3)$

Possible Answers:

$-3\sqrt2+2$

$\sqrt2-2$

$-\sqrt2-2$

Correct answer:

$-\sqrt2-2$

Explanation:

Use the FOIL method to simplify the binomials.

$(\sqrt{2}-2)(\sqrt{8}+3) = \sqrt{2}(\sqrt{8})+\sqrt{2}(3)+(-2)(\sqrt{8})+(-2)(3)$

Simplify the terms.

$=\sqrt{16}+3\sqrt2-2\sqrt8-6$

$=\sqrt{16}+3\sqrt2-2(\sqrt4 \times \sqrt2)-6$

$=4+3\sqrt2-2(2\sqrt2)-6$

$=4+3\sqrt2-4\sqrt2-6$

Combine like-terms.

The answer is: $-\sqrt2-2$

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Example Question #81 : Quadratic Equations And Inequalities

Solve: (3x-5)(4-x)

Possible Answers:

-3x^2-24x-20

-3x^2+17x-20

-3x^2-17x-20

-3x^2-7x-20

-3x^2+7x-20

Correct answer:

-3x^2+17x-20

Explanation:

Use the FOIL method to expand the binomials.

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

The expression becomes:

(3x)(4)+(3x)(-x)+(-5)(4)+(-5)(-x)

Simplify by distribution.

12x-3x^2-20+5x

Combine like-terms.

The answer is: -3x^2+17x-20

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Example Question #241 : Intermediate Single Variable Algebra

Simplify: $(\sqrt{12}-\sqrt{6})(\sqrt{3}+\sqrt{24})$

Possible Answers:

$6-9\sqrt2$

$2-9\sqrt6$

$9\sqrt2 -6$

$15\sqrt2 +18$

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

Correct answer:

$9\sqrt2 -6$

Explanation:

Simplify by using the FOIL method.

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

Use this formula to solve the binomials.

$(\sqrt{12}-\sqrt{6})(\sqrt{3}+\sqrt{24})$

$(\sqrt{12})(\sqrt{3})+(\sqrt{12})(\sqrt{24})+(-\sqrt{6})(\sqrt{3})+(-\sqrt{6})(\sqrt{24})$

To avoid simplifying large radicals at the end, we should factor some of the radicals before simplifying the terms.

$(\sqrt{12})(\sqrt{3})+(\sqrt{4}\times \sqrt{3})(\sqrt{4}\times \sqrt{6})+(-\sqrt{6})(\sqrt{3})+(-\sqrt{6})(\sqrt{4}\times \sqrt{6})$

The expression becomes:

$\sqrt{36}+(2\times \sqrt{3})(2\sqrt{6})+(-\sqrt{6})(\sqrt{3})+(-\sqrt{6})(2 \sqrt{6})$

Simplify all the terms.

$6+4\sqrt{18}-\sqrt{18}+12=6+3(\sqrt9\times \sqrt{2})-12$

$=6+3(3\sqrt{2})-12 = 9\sqrt2 -6$

The answer is: $9\sqrt2 -6$

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Example Question #85 : Understanding Quadratic Equations

Solve: (5x-10)(2x+8)

Possible Answers:

10x^2-40x-80

10x^2+60x-80

10x^2+40x-80

10x^2+20x-80

10x^2-20x-80

Correct answer:

10x^2+20x-80

Explanation:

Use the FOIL method to solve this expression.

(w+x)(y+z) = wy+wz+xy+xz

Use the template to rewrite the expression.

(5x)(2x)+(5x)(8)+(-10)(2x)+(-10)(8)

Simplify the terms.

10x^2+40x-20x-80

Combine like-terms.

The answer is: 10x^2+20x-80

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Example Question #62 : Foil

Solve: $(8x-6)(\frac{1}{x}+3)$

Possible Answers:

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

$\frac{24x^2+2x-6}{x}$

$\frac{8x^2+2x-18}{x}$

$\frac{24x^2-10x-6}{x}$

$\frac{24x^2+10x-6}{x}$

Correct answer:

$\frac{24x^2-10x-6}{x}$

Explanation:

Use the FOIL method to simplify this expression.

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

Rewrite the expression.

$(8x)(\frac{1}{x})+(8x)(3)+ (-6)(\frac{1}{x})+(-6)(3)$

Simplify all terms.

$8+24x-\frac{6}{x}-18$

Combine like terms.

$24x-10-\frac{6}{x}$

Rewrite the expression using a common denominator.

$\frac{24x(x)}{x}-\frac{10(x)}{x}-\frac{6}{x}$

The answer is: $\frac{24x^2-10x-6}{x}$

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Example Question #81 : Understanding Quadratic Equations

Solve: (3x-7)(7x-1)

Possible Answers:

21x^2-46x+7

21x^2-52x+7

21x^2+52x+7

21x^2-46x-7

21x^2-52x-7

Correct answer:

21x^2-52x+7

Explanation:

Use the FOIL method to expand the terms of the binomials.

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

(3x)(7x)+(3x)(-1)+(-7)(7x)+(-7)(-1)

21x^2-3x-49x+7

Combine like terms.

The answer is: 21x^2-52x+7

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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 #59 : Foil

Example Question #60 : Foil

Example Question #61 : Foil

Example Question #81 : Quadratic Equations And Inequalities

Example Question #82 : Understanding Quadratic Equations

Example Question #81 : Quadratic Equations And Inequalities

Example Question #241 : Intermediate Single Variable Algebra

Example Question #85 : Understanding Quadratic Equations

Example Question #62 : Foil

Example Question #81 : Understanding Quadratic Equations

All Algebra II Resources

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