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Algebra II : Solving Expressions

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Example Question #21 : Solving Expressions

If f(x)= 2x^2+1 and g(x)=x-3 , what is f(g(2)) ?

Possible Answers:

Correct answer:

Explanation:

To begin solving, first we would plug in to g(x) for every there is, making it:

g(2)=(2)-3

Solving, we get:

g(2)=-1

We would then put that solution into f(x) for every there is, making it:

$f(g(2))=2(-1)^{2}+1$

Following the order of operations, the first thing we do is square :

$-1 \times -1 = 1$

We can then solve the rest of the expression:

f(g(2))=2(1)+1

f(g(2))=3

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Example Question #22 : Solving Expressions

Solve the expression: -6(x-6)^2-3x+2

Possible Answers:

-6x^2-75x+218

-6x^2+69x-216

-6x^2+69x-218

-6x^2-69x+214

-6x^2+69x-214

Correct answer:

-6x^2+69x-214

Explanation:

Evaluate the binomial squared first by order of operations.

(x-6)^2 = (x-6)(x-6)

= x(x)+(x)(-6)+(-6)(x)+(-6)(-6)

x^2-12x+36

The expression becomes:

-6(x^2-12x+36)-3x+2

Distribute the negative six through each term of the trinomial.

-6x^2+72x-216-3x+2

Combine like-terms.

The answer is: -6x^2+69x-214

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Example Question #23 : Solving Expressions

Solve the expression if a=3 : 6a(a^2-a^3)

Possible Answers:

324

648

Correct answer:

Explanation:

Substitute the value of into the given expression.

6(3)((3)^2-(3)^3)

Simplify the parentheses by order of operations.

18(9-27) = 18(-18) = -324

The answer is:

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Example Question #24 : Solving Expressions

If a=5 and b=6 , evaluate: $\frac{1}{b}-\frac{b}{a}$

Possible Answers:

$-\frac{19}{30}$

$-\frac{29}{30}$

$-\frac{2}{5}$

$-\frac{31}{30}$

$-\frac{41}{30}$

Correct answer:

$-\frac{31}{30}$

Explanation:

Substitute the assigned values into the expression.

$\frac{1}{b}-\frac{b}{a} = \frac{1}{6}-\frac{6}{5}$

Convert the fractions to a common denominator.

$\frac{1}{6}-\frac{6}{5} = \frac{1(5)}{6(5)}-\frac{6(6)}{5(6)} = \frac{5}{30}- \frac{36}{30}$

Now that the denominators are common, the numerators can be subtracted.

The answer is: $-\frac{31}{30}$

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Example Question #25 : Solving Expressions

If a=4 and b=6 , determine: a(2-b)-a

Possible Answers:

Correct answer:

Explanation:

Substitute the values into the expression.

a(2-b)-a = 4(2-6)-4

Simplify the expression by distribution.

4(2-6)-4 = 4(-4)-4 = -16-4 = -20

The answer is:

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Example Question #26 : Solving Expressions

If $a=\sqrt5, b=\sqrt3$ , what is the value of $\frac{15}{ab}$ ?

Possible Answers:

$\frac{\sqrt{15}}{2}$

$2\sqrt{15}$

$\sqrt{30}$

$\sqrt{15}$

$\frac{\sqrt{15}}{15}$

Correct answer:

$\sqrt{15}$

Explanation:

Substitute the values of and .

$\frac{15}{\sqrt{5}\cdot \sqrt{3}} = \frac{15}{\sqrt{15}}$

Rationalize the denominator by multiplying the top and bottom with the denominator. This will eliminate the radical in the denominator.

$\frac{15}{\sqrt{15}}\cdot \frac{\sqrt{15}}{\sqrt{15}}=\frac{15\sqrt{15}}{15}$

Cancel the integers.

The answer is: $\sqrt{15}$

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Example Question #27 : Solving Expressions

Solve the expression: 3a^2-9b^3 if a=6 and b=2

Possible Answers:

108

Correct answer:

Explanation:

In order to solve this expression, we will need to substitute the assigned values into and .

3a^2-9b^3 = 3(6)^2-9(2)^3

Simplify the terms by order of operation.

3(6)^2-9(2)^3 = 3(36)-9(8) = 108-72=36

The answer is:

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Example Question #28 : Solving Expressions

If a=5 and b =-3 , what is 2a^2-4b^3 ?

Possible Answers:

158

Correct answer:

158

Explanation:

Substitute the values into the expression.

2a^2-4b^3 = 2(5)^2-4(-3)^3

Simplify the terms by order of operations.

2(5)^2-4(-3)^3 = 2(25) - 4(-27)

=50 + 108=158

The answer is: 158

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Example Question #29 : Solving Expressions

If a=6 and b=-6 , what is the value of $-a^{-2}-b^{-2}$ ?

Possible Answers:

$-\frac{1}{18}$

$-\frac{1}{36}$

$-\frac{1}{72}$

Correct answer:

$-\frac{1}{18}$

Explanation:

Substitute the values into the expression.

$-(6)^{-2}-(-6)^{-2}$

In order to evaluate this expression, we will need to rewrite the negative exponents into fractions.

$-(6)^{-2}-(-6)^{-2}= -\frac{1}{6^2}-\frac{1}{(-6)^2}$

Simplify the fractions.

$-\frac{1}{36}-\frac{1}{36} =- \frac{2}{36}$

Reduce this fraction.

The answer is: $-\frac{1}{18}$

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Example Question #30 : Solving Expressions

If a=3 and b=2 , what is the value of $\frac{b}{\sqrt a}$ ?

Possible Answers:

$\frac{2\sqrt{3}}{3}$

$\frac{3\sqrt{3}}{2}$

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

$\frac{3\sqrt{2}}{2}$

$3\sqrt2$

Correct answer:

$\frac{2\sqrt{3}}{3}$

Explanation:

Substitute the values in the expression.

$\frac{b}{\sqrt a} = \frac{2}{\sqrt 3}$

Rationalize the denominator by multiplying square root of three on the top and bottom of the fraction.

$\frac{2}{\sqrt 3}\cdot \frac{\sqrt 3}{\sqrt 3}$

Simplify the top and bottom.

The answer is: $\frac{2\sqrt{3}}{3}$

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Algebra II : Solving Expressions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #21 : Solving Expressions

Example Question #22 : Solving Expressions

Example Question #23 : Solving Expressions

Example Question #24 : Solving Expressions

Example Question #25 : Solving Expressions

Example Question #26 : Solving Expressions

Example Question #27 : Solving Expressions

Example Question #28 : Solving Expressions

Example Question #29 : Solving Expressions

Example Question #30 : Solving Expressions

All Algebra II Resources

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