Multiplying and Dividing Polynomials - Pre-Algebra

Use the distributive property:

Multiply making sure to distribute the negative sign:

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:

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 .

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.

This product fits the sum of cubes pattern, where :

So

Use FOIL (First Outer Inner Last).

Use FOIL to expand the polynomial.

First factor each equation fully to see if there are terms that can cancel out:

Cancel terms:

Simplify exponents:

Variables without any exponents have an invisable 1 as their exponent.

In order to simplify this, we need to rewrite the numerator by factorization.

To factor the numerator, we need to look at the factors of the integer value. The factors of the integer value when added together should result in the middle term of the polyinomial. In this particular case there is no middle term therefore, we are looking for a factor that when added together results in a zero term. This is also known as the differences of squares.

Cancel the terms in the numerator and denominator.

The correct answer is:

In order to divide this polynomial, it is necessary to factor out the numerator.

To factor this polynomial find the two factors of the integer term, , that when added together results in the middle term of the polynomial, .

This particular type of polynomial is known as the difference of perfect squares.

Use the distributive property to expand this expression. When powers of similar bases are multiplied, their powers can be added.

Use the FOIL method to simplify. FOIL stands for the finding the product of polynomials by multiplying their First, Outer, Inner, and Last terms together.

Firsts:

Outers:

Inners:

Lasts:

Multiply out each term and adding them results in the final polynomial.

Remember when multiplying like bases you add their exponents.

Use the distributive property to expand the expression.

Use the FOIL method to expand the terms.

Multiply out each term.

Combine like-terms and write out the expanded form.

The answer is:

When dividing with exponents that have different bases, divide the bases then subtract the exponents.

To figure out the solution to this problem is to simply multiply the integers normally so

The rule to multiply the same variables with exponents is to add the exponents together. For example,

So,