Multiplication of polynomials will be done as per the following steps.

- Multiply each term in the first polynomial by each term in another polynomial.
- Combine the like terms and add them.

Here are examples of multiplication of monomials, binomials as well as the polynomials.

**Monomial with Monomial [ 1 term * 1 term ]**

To multiply one monomial by another monomial, we have to first multiply the constant, then multiply each variable together and then combine the results.

**Example: **(4xy )(8y)

**Solution: **(4xy)(8y) = 4.8.xy.y =

## Monomial with Binomial [ 1 term * 2 terms]

To multiply one monomial with the binomial term, we have to multiply single term with each of two-term and then combine the results.

**Example: **5y( y + 3yz)

**Solution: **5y( y + 3yz) = 5y.y + 5y.3yz =

## Binomial with Monomial [ 2 terms * 1 term]

To multiply binomial term with monomial, just multiply each term of binomial with the single term and then combine the results.

**Example: **

**Solution:** =

## Binomial with Binomial [ 2 terms * 2 terms]

To multiply two binomial, we have to follow the concept of FOIL (First Outer Inner Last) method and then combine the like terms and add them.

**Example: **(x+4) (x+8)

- The F stands for first, which means the x in the first factor times the x in the second factor.
- The O stands for outer, which means the x in the first factor times the 8 in the second factor.
- The I stands for inner, which means the 4 in the first factor times the x in the second factor.
- The L stands for last, which means the 4 in the first factor times the 8 in the second factor.

**Solution: **(x+4) (x+8) = =

## Binomial with Trinomial [ 2 terms * 3 terms]

Here FOIL doesn’t work, beacuse there are more terms. Following are the steps to multiply a 2 term polynomial with trinomial term.

- Take the first term in polynomial one and multiply it with every term in the second polynomial
- Follow the rule of changing sign while multiplying.
- Take the second term in polynomial one and multiply it with every term in the second polynomial
- Follow the rule of changing sign while multiplying.
- Now combine the like terms to obtain the result.

**Example: **

**Solution: ** = = =

## Exercise

Multiply the following polynomials

Sandy Saves says

this was helpful

However, check the answer to your example for a monomial times a monomial. I believe that the coefficient should be 32, not 12.