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Algebra II : Understanding Quadratic Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #71 : Quadratic Equations And Inequalities

Solve: $(\pi-3)(1-3\pi)$

Possible Answers:

$-3\pi^2-10\pi-3$

$-3\pi^2+8\pi-3$

$-3\pi^2-8\pi-3$

$4\pi^2-10$

$-3\pi^2+10\pi-3$

Correct answer:

$-3\pi^2+10\pi-3$

Explanation:

We can expand this expression by using the FOIL method.

Follow the given template and substitute.

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

$(\pi-3)(1-3\pi)$

$=(\pi)(1)+(\pi)(-3\pi)+(-3)(1)+(-3)(-3\pi)$

Simplify the terms.

$=\pi-3\pi^2-3+9\pi$

Combine like-terms.

The answer is: $-3\pi^2+10\pi-3$

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Example Question #231 : Intermediate Single Variable Algebra

Solve the expression: (4-x)(7+6x)

Possible Answers:

-6x^2+17x+28

-6x^2-31x+28

-6x^2-17x+28

-6x^2-12x+38

-6x^2+31x+28

Correct answer:

-6x^2+17x+28

Explanation:

Use the FOIL method to simplify this expression.

Multiply each term of the first binomial with the terms of the second binomial.

(4)(7) + (4)(6x) + (-x)(7) + (-x)(6x)

Simplify the expression.

28+24x-7x-6x^2

Combine like terms.

The answer is: -6x^2+17x+28

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Example Question #71 : Quadratic Equations And Inequalities

Evaluate: $(\sqrt{3}-3)(\sqrt5-5)$

Possible Answers:

$-7\sqrt5 +15$

$\sqrt{15}-5\sqrt3 -3\sqrt5 +15$

$\sqrt{15}-8\sqrt3 +15$

$-7\sqrt{15} +15$

$\sqrt{15}-8\sqrt5 +15$

Correct answer:

$\sqrt{15}-5\sqrt3 -3\sqrt5 +15$

Explanation:

Use the FOIL method to simplify this expression. Use the following template:

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

$(\sqrt{3}-3)(\sqrt5-5)$

$= (\sqrt{3})(\sqrt{5 })+(\sqrt{3})(-5)+(-3)(\sqrt{5})+(-3)(-5)$

Simplify each term. Uncommon radical terms cannot be combined.

The answer is: $\sqrt{15}-5\sqrt3 -3\sqrt5 +15$

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Example Question #55 : Foil

Evaluate: (x^2+3)(-9x^2+4)

Possible Answers:

-9x^4+23x^2+12

-9x^4-16x^2+12

-9x^4-23x^2+12

-9x^4-48x^2+12

-9x^4-31x^2+12

Correct answer:

-9x^4-23x^2+12

Explanation:

Use the FOIL method to simplify this expression. Use the following formula as a template to solve the expression:

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

For (x^2+3)(-9x^2+4) ,

(x^2)(-9x^2)+(x^2)(4)+(3)(-9x^2)+(3)(4)

Simplify all the terms.

-9x^4+4x^2-27x^2+12

Combine like terms.

The answer is: -9x^4-23x^2+12

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Example Question #56 : Foil

Simplify the binomials: $(\frac{2}{3}x+3)(\frac{2}{5}x+2)$

Possible Answers:

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

$\frac{4}{15}x^2+\frac{14}{5}x+6$

$\frac{1}{2}x^2+\frac{38}{15}x+6$

$\frac{1}{2}x^2+\frac{14}{5}x+6$

$\frac{4}{15}x^2+\frac{38}{15}x+6$

Correct answer:

$\frac{4}{15}x^2+\frac{38}{15}x+6$

Explanation:

Use the FOIL method to simplify this expression.

$(\frac{2}{3}x+3)(\frac{2}{5}x+2)$

$=(\frac{2}{3}x)(\frac{2}{5}x)+(\frac{2}{3}x)(2)+(3)(\frac{2}{5}x)+(3)(2)$

Simplify all the terms in parentheses.

$\frac{4}{15}x^2+\frac{4}{3}x+\frac{6}{5}x+6$

Combine the center two terms.

$\frac{4}{3}x+\frac{6}{5}x = \frac{20}{15}x+\frac{18}{15}x = \frac{38}{15}x$

The answer is: $\frac{4}{15}x^2+\frac{38}{15}x+6$

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Example Question #57 : Foil

Evaluate: (4x-6)(7x+3)

Possible Answers:

28x^2+54x-18

28x^2+30x-18

28x^2-54x-18

28x^2-30x-18

28x^2-46x-18

Correct answer:

28x^2-30x-18

Explanation:

Use the FOIL method to simplify this expression.

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

Follow this equation for the given problem.

(4x-6)(7x+3) = (4x)(7x)+(4x)(3)+(-6)(7x)+(-6)(3)

Simplify the parentheses.

28x^2+12x-42x-18

Combine like-terms.

The answer is: 28x^2-30x-18

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Example Question #58 : Foil

Solve: (5x+18)(3x-1)

Possible Answers:

15x^2+49x-18

15x^2-59x-18

15x^2+59x-18

15x^2-49x-18

15x^2-3x-18

Correct answer:

15x^2+49x-18

Explanation:

Solve the expression by using the FOIL method. Follow the template below.

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

(5x)(3x)+(5x)(-1)+(18)(3x)+(18)(-1)

Simplify the terms.

15x^2-5x+54x-18

Combine like-terms.

15x^2-5x+54x-18 = 15x^2+49x-18

The answer is: 15x^2+49x-18

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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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Algebra II : Understanding Quadratic Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #71 : Quadratic Equations And Inequalities

Example Question #231 : Intermediate Single Variable Algebra

Example Question #71 : Quadratic Equations And Inequalities

Example Question #55 : Foil

Example Question #56 : Foil

Example Question #57 : Foil

Example Question #58 : Foil

Example Question #59 : Foil

Example Question #60 : Foil

Example Question #61 : Foil

All Algebra II Resources

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