# Algebra 1 : How to multiply polynomials

## Example Questions

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Multiply:

Explanation:

Multiply:

Explanation:

### Example Question #101 : Variables

Write as a polynomial in standard form:

Explanation:

Replace: :

### Example Question #1 : Multiplication And Division

Multiply:

Explanation:

The first two factors are the product of the sum and the difference of the same two terms, so we can use the difference of squares:

Now use the FOIL method:

### Example Question #11 : How To Multiply Polynomials

Simplify the expression.

Explanation:

Rearrange the expression so that the  and  variables of different powers are right next to each other.

When multiplying the same variable with different exponents, it is the same as adding the exponents: . Taking advantage of this rule, the problem can be rewritten.

### Example Question #42 : Polynomial Operations

Rewrite as a single radical expression, assuming  is positive:

Explanation:

Rewrite each radical as an exponential expression, apply the product of powers property, and rewrite the product as a radical:

### Example Question #43 : Polynomial Operations

Evaluate:

Explanation:

This set is out of order, and it may be best to reorganize the terms.  To solve, this is very similar to the FOIL method.

Follow the procedure to distribute each term.

Follow suit to solve the problem.

Combine like terms.

### Example Question #44 : Polynomial Operations

Multiply and simplify the expression
.

Explanation:

The question is asking for the simplified version of this expression:

First, combine like terms in the numerator and denominator according to multiplication and exponent rules. When you are multiplying like bases together you add their exponents.

When you divide like bases you subtract the bottom exponent from the top exponent.

Finally, simplify the expression by cancelling out terms using GCFs.

### Example Question #45 : Polynomial Operations

Multiply the polynomials and simplify:

Explanation:

The key to multiplying polynomials is to keep track of signs and be absolutely sure that you multiply every term in one polynomial (choose the first one) by every term in the other polynomial. For example if polynomial A has 3 terms and polynomial B has two, then then start with the first term in polynomial A and multiply it by both terms in polynomial B. Then choose the second term in polynomial A and repeat. Continue like so until you have gone through all iterations.

First term:

Second term:

Third term:

Now combine terms where able for the final answer:

Multiply: