# High School Math : Intermediate Single-Variable Algebra

## Example Questions

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### Example Question #1 : Polynomials

If and , what is ?

Explanation:

is a composite function where  is plugged into :

### Example Question #1 : Intermediate Single Variable Algebra

Simplify the following expression:

.

Explanation:

First, multiply out the second expression so that you get .

Then, multiply your like terms, taking care to remember that when multiplying terms that have the same base, you add the exponents. Thus, you get .

### Example Question #1 : Polynomials

Simplify:

Explanation:

Focus on each pair of like terms. The  completely cancel out, there is one  left on top, and five  left on the bottom.

reduces to .

Put that all together to get

### Example Question #1 : Multiplying And Dividing Exponents

Simplify.

Explanation:

Put the negative exponent on the bottom so that you have  which simplifies further to .

### Example Question #1 : Intermediate Single Variable Algebra

Expand this expression:

Explanation:

Use the FOIL method (First, Outer, Inner, Last):

Put all of these terms together:

Combine like terms:

### Example Question #6 : Polynomials

Simplify the following polynomial:

Explanation:

To simplify the polynomial, begin by multiplying the first binomial by every term within the parentheses:

Now, combine like terms:

Convert the polynomial into fraction form:

### Example Question #1 : Simplifying Polynomials

Simplify the following polynomial:

Explanation:

To simplify the polynomial, begin by rearranging the terms to have positive exponents:

Now, combine like terms:

Simplify the integers:

### Example Question #1 : Simplifying Polynomials

Simplify the following polynomial:

Explanation:

Squaring the polynomial is equivalent to:

Use the FOIL method to multiply the terms:

F - First

O - Outer

I - Inner

L - Last

Combine like terms:

### Example Question #1 : Intermediate Single Variable Algebra

Simplify the following polynomial:

Explanation:

To simplify the polynomial, begin by rearranging the terms to have positive exponents:

Rearrange the terms once again so that the outer exponent is positive. Also, combine like terms:

Now, square the polynomial:

### Example Question #1 : Polynomials

Simplify the following polynomial: