# Algebra II : Polynomials

## Example Questions

### Example Question #1 : How To Multiply Trinomials

Multiply the expressions:

Explanation:

You can look at this as the sum of two expressions multiplied by the difference of the same two expressions. Use the pattern

,

where  and .

To find , you use the formula for perfect squares:

,

where  and .

Substituting above, the final answer is .

### Example Question #11 : Polynomials

Simplify:

Explanation:

First, factor the numerator of the quotient term by recognizing the difference of squares:

Cancel out the common term from the numerator and denominator:

FOIL (First Outer Inner Last) the first two terms of the equation:

Combine like terms:

Explanation:

Expand:

Explanation:

### Example Question #13 : Simplifying Polynomials

Simplify

Explanation:

The polynominal breaks down to , and once you factor out a  from the denomintator and cancel, you are left with .

### Example Question #14 : Simplifying Polynomials

Simplify

Explanation:

First, you FOIL the binomial in the numerator. Then combine like terms, which simplifies the numerator to , which can be further simplified to . The coefficients for this can be found in Pascal's Triangle, so they do not have to be memorized. Once the numerator and denominator are in the same base, the exponents cancel out, leaving you with the correct answer.

### Example Question #15 : Simplifying Polynomials

Simplify the following expression

Expresion cannot be simplified any further

Explanation:

Simplify a polynomial expression by combining like terms. Like terms are those that have exactly the same variable and degree (exponent). This one is reasonably simple with only addition and subtraction of polynomials involved. The like terms are...

The remaining terms are  and

Combine everything together as done below. As long as the signs are right, order of operations lets you arrange the final answer various ways, but you should know this be able to identify the correct answer even if yours was arranged differently.

### Example Question #11 : Simplifying Polynomials

Simplify

Explanation:

To simplify you combind like terms:

### Example Question #114 : Polynomials

Simplify.

Explanation:

Simplify

Distribute the negative:

Then combinde like terms