When multiplying a whole number by a polynomial, we simply multiply that number by whatever coefficient is present in front of the variables of the polynomial. We then maintain the variables in the simplified expression.

Multipying a monomial and trinomial boils down to distributing the monomial amongst all the parts of the trinomial as such:

After some cleanup we get:

Distribute to each term within parentheses.

Putting it back together...

To expand, multiply 8x by both terms in the expression (3x + 7).

8x multiplied by 3x is 24x².

8x multiplied by 7 is 56x.

Therefore, 8x(3x + 7) = 24x² + 56x.

When multiplying, the order in which you multiply does not matter. Let's start with the first two monomials.

Use FOIL to expand.

Now we need to multiply the third monomial.

Similar to FOIL, we need to multiply each combination of terms.

Combine like terms.

Write the expression of the multiplied terms.

Distribute the monomial with each term in the polynomial.

Simplify this expression.

The answer is:

To divide this, we must pull out a common factor from the numerator and denominator.

The common factor from the numerator is only .

The common factor from the denominator is .

The only term that will cancel is the . We cannot cancel the inside and terms because they are different entities of a quantity.

The answer is:

When similar bases are multiplied, their powers can be added. Distribute the monomial through the polynomial in the parentheses.

The answer is:

Distribute to each of the terms within the parentheses.

Putting it back together...

When multiplying a polynomial and a monomial, distribute the monomial into the polynomial:

Then simplify and the answer is: