Algebra II - Solving Expressions

If , simplify $x^{2}+3x-4$ .

Explanation

First, you substitute for : $(4^{2})+3(4)-4$

Next, use PEMDAS (Parentheses, Exponents, Multiplication, Dividion, Addition, and Subtraction) to preform the algebraic operations in the correct order. When we apply this rule to simplify we get the following:

Simplify $z^{3}+x^{4}y^{2}-y^{3}+13$ given and .

Explanation

First, substitute 1 for z, 2 for x and 3 for y: $1^{3}+2^{4}3^{2}-3^{3}+13$ and simplify: $1+16\cdot9-27+13$ .

Using PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction), we simplify the multiplication: .

Then add and subtract from left to right: .

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

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

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

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

$3\sqrt2$

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

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

Evaluate the expression $3b-2a^{2}+c$ when , , and .

Explanation

First, substitute for , for , and for : $3(8)-2(4)^{2}+(25)$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

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

$-\frac{1}{18}$

$-\frac{1}{36}$

$-\frac{1}{72}$

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: $-\frac{1}{18}$

If and , what is ?

Explanation

Substitute the values into the expression.

Simplify the terms by order of operations.

The answer is:

Evaluate the expression $5^{x}-2x+6x-b$ when and .

Explanation

First, substitute for and for : $5^{3}-2(3)+6(3)-(8)$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

Solve the expression: if and

Explanation

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

Simplify the terms by order of operation.

The answer is:

Evaluate the expression when and .

Explanation

First, substitute for and for :

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

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

$\sqrt{15}$

$\sqrt{30}$

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

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

$2\sqrt{15}$

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: $\sqrt{15}$

Solving Expressions

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