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Algebra II : Expressions

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Example Questions

Example Question #61 : Simplifying Expressions

Simplify: $7ab^2(a^2-b^{-2})$

Possible Answers:

7a^3b^2-7a

$a^3b^2-\frac{a}{b^4}$

a^3b^2-a

7a^3b^2

$7a^3b^2-\frac{7a}{b^4}$

Correct answer:

7a^3b^2-7a

Explanation:

Distribute the outer term with both terms inside the parentheses.

$7ab^2(a^2-b^{-2}) = (7ab^2)(a^2)- (7ab^2)(b^{-2})$

When similar bases are multiplied, we can add the exponents of that base.

Simplify the terms.

$(7ab^2)(a^2)- (7ab^2)(b^{-2}) = 7a^3b^2- 7ab^0$

Any term besides zero raised to the power of zero equals one.

The answer is: 7a^3b^2-7a

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Example Question #151 : Basic Single Variable Algebra

Given the expression $\frac{w}{x}-\frac{w}{y}-\frac{w}{z}$ , what must be the numerator of the simplified form?

Possible Answers:

wyz-wxz-wxy

xyz-wyz-wxz

yz+xz+xy

yz-xz-xy

Correct answer:

wyz-wxz-wxy

Explanation:

To determine the number, we will need to find the least common denominator by multiplying all three denominators together.

(x)(y)(z)=xyz

Simplify the fractions.

$\frac{w}{x}-\frac{w}{y}-\frac{w}{z} = \frac{wyz}{xyz}-\frac{wxz}{xyz}-\frac{wxy}{xyz}$

The answer is: wyz-wxz-wxy

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Example Question #1995 : Algebra Ii

If a=-2 and b=-3 , what does (a+b)^2-(a-b)^2 equal?

Possible Answers:

Correct answer:

Explanation:

Substitute the terms into the expression.

(a+b)^2-(a-b)^2 = ((-2)+(-3))^2-((-2)-(-3))^2

Simplify the terms by order of operation. Start with the inner parentheses.

(-5)^2-(1)^2 = 25-1 = 24

The answer is:

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Example Question #152 : Basic Single Variable Algebra

Simplify: abc^2(ac-bc^2)

Possible Answers:

2abc^2-4bc

2a^2bc^3-2ab^2c^4

2abc^2-bc

a^2bc^3-ab^2c^4

a^2bc^3-2ab^2c^2

Correct answer:

a^2bc^3-ab^2c^4

Explanation:

In order to simplified the expression, we will need to distribute the outer term through the terms inside the parentheses.

abc^2(ac-bc^2)=abc^2(ac)-abc^2(bc^2)

Distribute the terms.

The answer is: a^2bc^3-ab^2c^4

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Example Question #153 : Basic Single Variable Algebra

Simplify: $\frac{\frac{y}{x(x+1)}}{1+\frac{y}{x(x+1)}}$

Possible Answers:

$\frac{x-y}{x^2+x+y}$

$\frac{y}{x+y}$

$\frac{x}{x+y}$

$\frac{y}{x^2+x+y}$

$\frac{x}{x^2+x+y}$

Correct answer:

$\frac{y}{x^2+x+y}$

Explanation:

Simplify the complex fraction by parts.

$\frac{y}{x(x+1) }= \frac{y}{x^2+x}$

Replace the terms.

$\frac{\frac{y}{x(x+1)}}{1+\frac{y}{x(x+1)}}=\frac{\frac{y}{x^2+x}}{1+\frac{y}{x^2+x}}$

Simplify the denominator. Convert the integer using the least common denominator, which is x^2+x .

$1+\frac{y}{x^2+x}=\frac{x^2+x}{x^2+x}+\frac{y}{x^2+x} = \frac{x^2+x+y}{x^2+x}$

Replace this term in the denominator.

$\frac{\frac{y}{x^2+x}}{1+\frac{y}{x^2+x}}=\frac{\frac{y}{x^2+x}}{ \frac{x^2+x+y}{x^2+x}}$

Rewrite this using a division sign.

$\frac{\frac{y}{x^2+x}}{ \frac{x^2+x+y}{x^2+x}} = \frac{y}{x^2+x} \div\frac{x^2+x+y}{x^2+x}$

Change the sign to multiplication and take the reciprocal of the second term.

$\frac{y}{x^2+x} \cdot \frac{x^2+x}{x^2+x+y}$

Cancel the common terms.

The answer is: $\frac{y}{x^2+x+y}$

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Example Question #2001 : Algebra Ii

Evaluate a^2+b^2 if 2a+2 =4 and b=5 .

Possible Answers:

Correct answer:

Explanation:

The value of will need to be solved for. Subtract two from both sides given the following equation.

2a+2 =4

2a+2 -2=4-2

2a=2

Divide by two on both sides.

$\frac{2a}{2}=\frac{2}{2}$

a=1

Now that we know the value of a and b, we substitute both values in the expression a^2+b^2 .

a^2+b^2 = 1^2+5^2 = 1+25= 26

The answer is:

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Example Question #111 : Expressions

Simplify: $\frac{b}{a^2}(a^2b-2a)$

Possible Answers:

$b^2-\frac{2b}{a}$

$b-\frac{2}{a}$

$b-\frac{2b}{a}$

a^2b^2-1

$2b-\frac{2b}{a}$

Correct answer:

$b^2-\frac{2b}{a}$

Explanation:

Distribute the fraction through both terms in the parentheses.

$\frac{b}{a^2}(a^2b-2a)=\frac{b}{a^2}(a^2b)-\frac{b}{a^2}(2a)$

Simplify the terms.

The answer is: $b^2-\frac{2b}{a}$

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Example Question #72 : Simplifying Expressions

Factor this expression: x^2 - 4x - 12

Possible Answers:

(x + 6) (x - 2)

Cannot be factored

(x + 2) (x - 3)

(x + 2) (x - 6)

(x + 2) (x - 4)

Correct answer:

(x + 2) (x - 6)

Explanation:

When we factor, we have to remember to check the signs in the trinomial. In this case, we have minus 4 and minus 12. That automatically tells us the signs in the factors must be opposite, one plus and one minus.

Next, we ask ourselves what are the factors of 12? We get 2 & 6, 1 & 12, and 4 & 3.

Then, we ask ourselves, which of these, when subtracted in a given order, will give us -4? The answer is 6 and 2! So we place these in the parentheses with the 's that we know go there so it looks like

$\left ( x\ \ \ 2 \right )\left ( x\ \ \ 6 \right )$

Finally, we ask ourselves, what signs do we need to put in to get negative 4 and negative 12? We need a positive but a negative so we put the addition sign in with the 2 and the negative sign in with the 6!

$\left ( x+2 \right )(x-6)$

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Example Question #163 : Basic Single Variable Algebra

Given that $x\neq 0$ or , simplify:

$\frac{1+\frac{1}{x}}{x+1}$

Possible Answers:

(x+1)^2

$\frac{1}{x}$

x+1

Correct answer:

$\frac{1}{x}$

Explanation:

Step 1: Find a common denominator for terms in numerator

$\frac{1+\frac{1}{x}}{x+1}=\frac{\frac{x}{x}+\frac{1}{x}}{x+1}=\frac{\frac{x+1}{x}}{x+1}$

Step 2: Divide

$\frac{\frac{x+1}{x}}{x+1}=\frac{x+1}{x}*\frac{1}{x+1}=\frac{1}{x}$

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Example Question #1 : Solving Expressions

Solve for x.

3x(8)-5=-2(3x+5)

Possible Answers:

-1/6

-5/18

1/6

Correct answer:

-1/6

Explanation:

a. Simplify each side of the equation using the distributive property.

24x-5=-6x-10

b. Add 6x to both sides of the equation to move all terms with "x" to the left side of the equation.

30x-5=-10

c. Add 5 to both sides of the equation to move all constants to the right side of the equation.

30x=-5

d. Divide both sides of the equation by 30 to isolate the variable. Simplify the resulting fraction

x=-5/30=-1/6

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Algebra II : Expressions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #61 : Simplifying Expressions

Example Question #151 : Basic Single Variable Algebra

Example Question #1995 : Algebra Ii

Example Question #152 : Basic Single Variable Algebra

Example Question #153 : Basic Single Variable Algebra

Example Question #2001 : Algebra Ii

Example Question #111 : Expressions

Example Question #72 : Simplifying Expressions

Example Question #163 : Basic Single Variable Algebra

Example Question #1 : Solving Expressions

All Algebra II Resources

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