# Pre-Algebra : Multiplying and Dividing Polynomials

## Example Questions

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

Multiply:

Explanation:

Multiply making sure to distribute the negative sign:

Multiply:

Explanation:

### Example Question #3 : Multiplying And Dividing Polynomials

Simplify:

Explanation:

When multiplying, remember the Product Rule of Exponents:

Step 1: Multiply the first term of the first polynomial across the terms of the second polynomial, and then add those products:

Step 2: Multiply the second term of the first polynomial across the terms of the second polynomial, and again add the products:

Step 3: Add the products from Step 1 and Step 2 by combining like terms.  Remember that variables with different exponents are not like terms. For example,  and  are like terms, but,  and  are not like terms:

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

Expand the following:

Explanation:

Recall that when expanding polynomials, we use the term FOIL (First, Outside, Inside, Last) to help us multiply all terms together.

Next, multiply each term to simplify and combine like terms. Note: Be careful with negative signs.

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

Simplify:

Explanation:

To solve, you can use the commutative and associative properties of multiplication to group like-terms together.

The 4 and 3 should be first multiplied, resulting in 12.

Next  should be multiplied by , giving us .

12 times  is equal to

Therefore, the correct answer is .

### Example Question #1 : Algebraic Concepts

Multiply:

Explanation:

Use the distributive property:

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

Multiply:

Explanation:

This product fits the sum of cubes pattern, where :

So

### Example Question #11 : Polynomials

Simplify:

Explanation:

Cancel by subtracting the exponents of like terms:

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

Simplify the following expression:

=

Explanation:

Use FOIL (First Outer Inner Last).

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

Expand the following expression: