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Algebra II : Quadratic Equations and Inequalities

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Example Questions

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Example Question #61 : Quadratic Equations And Inequalities

Solve: $(\sqrt{3}-\sqrt{2})(\sqrt2-\sqrt3)$

Possible Answers:

$\sqrt6-5$

$2\sqrt6-5$

$2\sqrt3-5$

$\sqrt6-1$

Correct answer:

$2\sqrt6-5$

Explanation:

Use the FOIL method to solve this problem.

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

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

Multiply the terms together.

$\sqrt6-3-2+\sqrt6$

Combine like-terms.

The answer is: $2\sqrt6-5$

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Example Question #62 : Quadratic Equations And Inequalities

Simplify: $(\sqrt{8}-3)(\sqrt8+6)$

Possible Answers:

$6\sqrt2-10$

$2\sqrt2+12$

$3\sqrt2-6$

$4\sqrt2-6$

$4\sqrt2-8$

Correct answer:

$6\sqrt2-10$

Explanation:

Solve the binomials by using the FOIL method. Following the template given:

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

$(\sqrt8)(\sqrt8)+(\sqrt8)(6)+(-3)(\sqrt8)+(-3)(6)$

Simplify the expression.

$8+6\sqrt8-3\sqrt8-18$

Combine like-terms.

$3\sqrt8 -10$

We can rewrite $\sqrt8$ using common factors.

$\sqrt8 =\sqrt 4\cdot \sqrt2 = 2\sqrt2$

$3(2\sqrt2) -10 = 6\sqrt2-10$

The answer is: $6\sqrt2-10$

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Example Question #63 : Quadratic Equations And Inequalities

Solve: (9-3x)(-2-8x)

Possible Answers:

24x^2+78x-18

24x^2-66x-18

24x^2-78x-18

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

24x^2+66x-18

Correct answer:

24x^2-66x-18

Explanation:

Solve this expression using the FOIL method.

Use the following template for the FOIL method:

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

Rewrite (9-3x)(-2-8x) .

(9)(-2)+(9)(-8x)+(-3x)(-2)+(-3x)(-8x)

Simplify the terms.

-18-72x+6x+24x^2

Combine like-terms and reorder the expression from highest to lowest power.

The answer is: 24x^2-66x-18

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Example Question #64 : Quadratic Equations And Inequalities

Solve: (e^2+3)(e-1)

Possible Answers:

-e^3-3

e^3-e^2+3e-3

e^3-2e^2-3

e^3+e^2-3e-3

e^3+4e^2-3e-3

Correct answer:

e^3-e^2+3e-3

Explanation:

Simplify by using the FOIL method. Follow the template below to solve the problem.

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

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

Simplify the terms.

e^3-e^2+3e-3

Do not combine unlike terms.

The answer is: e^3-e^2+3e-3

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Example Question #65 : Quadratic Equations And Inequalities

Expand: $(5-\sqrt8)(4-\sqrt2)$

Possible Answers:

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

$24-13\sqrt2$

$8-5\sqrt2$

$16-13\sqrt2$

Correct answer:

$24-13\sqrt2$

Explanation:

Use the FOIL method to solve this expression.

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

Write out the terms.

$(5-\sqrt8)(4-\sqrt2)$

$=(5)(4)+(5)(-\sqrt2)+(-\sqrt8)(4)+(-\sqrt8)(-\sqrt2)$

Simplify the terms.

$=20-5\sqrt2-4\sqrt8+\sqrt{16}$

Rewrite the radicals that are not simplified.

$\sqrt8 = \sqrt{4\times 2} = \sqrt4 \times \sqrt2 = 2\sqrt2$

$\sqrt{16}=4$

Replace the terms.

$=20-5\sqrt2-4(2\sqrt2)+4$

$= 20-5\sqrt2-8\sqrt2+4 = 24-13\sqrt2$

The answer is: $24-13\sqrt2$

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Example Question #66 : Quadratic Equations And Inequalities

Solve: (9x-8)(10x-7)

Possible Answers:

90x^2+17x+56

90x^2-17x+56

90x^2-143x-56

90x^2+143x-56

90x^2-143x+56

Correct answer:

90x^2-143x+56

Explanation:

Solve this by using the FOIL method.

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

Substitute the given terms by the given formula.

(9x-8)(10x-7)

= (9x)(10x)+ (9x)(-7)+(-8)(10x)+(-8)(-7)

Simplify the terms.

90x^2-63x-80x+56

Combine like-terms.

The answer is: 90x^2-143x+56

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Example Question #67 : Quadratic Equations And Inequalities

Solve: (-6+2x)(-9+3x)

Possible Answers:

6x^2-29x+54

6x^2-36x+54

-6x^2-36x+54

6x^2+54

6x^2-20x+54

Correct answer:

6x^2-36x+54

Explanation:

Use the FOIL method to expand the binomials.

(-6)(-9)+(-6)(3x)+(2x)(-9)+(2x)(3x)

Simplify the terms.

54-18x-18x+6x^2

Combine like terms.

The answer is: 6x^2-36x+54

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Example Question #68 : Quadratic Equations And Inequalities

Solve: (-2x+5)(3x-9)

Possible Answers:

-6x^2-2x-45

6x^2-20x-45

-6x^2-33x+45

-6x^2+3x-45

-6x^2+33x-45

Correct answer:

-6x^2+33x-45

Explanation:

Solve this expression by using the FOIL method.

(-2x)(3x)+(-2x)(-9)+(5)(3x)+(5)(-9)

Simplify each term by order of operations.

-6x^2+18x+15x-45

Combine like-terms.

The answer is: -6x^2+33x-45

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Example Question #69 : Quadratic Equations And Inequalities

Solve: $(\frac{1}{\sqrt2}-\sqrt2)(\frac{2}{\sqrt2}-\sqrt2)$

Possible Answers:

Correct answer:

Explanation:

Use the FOIL method to expand the terms. Follow the template for using this method.

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

$(\frac{1}{\sqrt2}-\sqrt2)(\frac{2}{\sqrt2}-\sqrt2)$

$(\frac{1}{\sqrt2})(\frac{2}{\sqrt2})+(\frac{1}{\sqrt2})(-\sqrt2)+(-\sqrt2)(\frac{2}{\sqrt2})+(-\sqrt2)(-\sqrt2)$

Simplify all the terms.

1-1-2+2 = 0

The answer is:

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Example Question #70 : Quadratic Equations And Inequalities

Solve: (7x-4)(3-9x)

Possible Answers:

-63x^2-15x-12

-63x^2-24x-12

-63x^2-57x-12

-63x^2-15x-12

-63x^2+57x-12

Correct answer:

-63x^2+57x-12

Explanation:

Use the FOIL method to simplify the expression. Multiply each term of the first binomial with the terms of the second binomial.

(7x)(3)+(7x)(-9x)+(-4)(3)+(-4)(-9x)

Simplify the expression.

21x-63x^2-12+36x

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

The answer is: -63x^2+57x-12

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Algebra II : Quadratic Equations and Inequalities

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #61 : Quadratic Equations And Inequalities

Example Question #62 : Quadratic Equations And Inequalities

Example Question #63 : Quadratic Equations And Inequalities

Example Question #64 : Quadratic Equations And Inequalities

Example Question #65 : Quadratic Equations And Inequalities

Example Question #66 : Quadratic Equations And Inequalities

Example Question #67 : Quadratic Equations And Inequalities

Example Question #68 : Quadratic Equations And Inequalities

Example Question #69 : Quadratic Equations And Inequalities

Example Question #70 : Quadratic Equations And Inequalities

All Algebra II Resources

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