How to multiply polynomials - Algebra

When multiplying exponential components, you must add the powers of each term together.

When multiplying polynomials, add the powers of each like-termed variable together.

For x: 5 + 2 = 7

For y: 17 + 2 = 19

Therefore the answer is .

The first step is to distribute the first term in the binomial across the trinomial:

Then multiply the second term in the binomial across the same trinomial:

You can then combine like terms to reach a simplified answer:

Use FOIL to expand the monomials.

Return this expansion to the original expression.

Distribute negative sign.

Combine like terms.

Distribute through every term in the parentheses.

This gives us the following:

First multiply each of the terms inside the second parentheses by :

Next multiply each of the terms inside the second parentheses by :

Finally multiply each of the terms inside the second parentheses by 5:

By combining all like terms we get the correct answer:

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.

Replace: :

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:

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

When we FOIL this expression, we start by multiplying the first term of the first binomial with the first term of the second binomial. Then we multiply the two "outside" terms (in this case those are and 4). Next we multiply the "inside" terms (in this case the two inside terms are and ) and finally the last terms.

When we combine terms in this way, it is important to make sure we are paying attention to the exponents! We want to add the exponents when we multiply terms. So, when multiplying , we want to add the 2 with 1 (the exponent of an un-powered variable is always 1!) and we get 3! So we know the resulting power would be 3, like this:

Using that skill and the FOIL technique, we end up with the answer,

When we FOIL this expression, we start by multiplying the first term of the first binomial with the first term of the second binomial. Then we multiply the two "outside" terms (in this case those are the and ). Next we multiply the "inside" terms (in this case the two inside terms are and ) and finally the last terms.

When we combine terms in this way, it is important to make sure we are paying attention to the exponents! When we multiply like terms with exponents, we can add the exponents together! In this case, we have an (which since it has no power, means it is to the power of 1) and an . We can add these exponents together when we go through our FOIL process and get . So we know the resulting power would be , like this:

Using that skill and the FOIL technique, we end up with the answer:

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.

The correct answer is:

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.

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 each term of the first polynomial with all the terms of the second polynomial. Follow the signs of the first polynomial.

Add and combine like terms.

The answer is: