You can look at this as the sum of two expressions multiplied by the difference of the same two expressions. Use the pattern

,

where and .

To find , you use the formula for perfect squares:

,

where and .

Substituting above, the final answer is .

We can accomplish this division by re-writing the problem as a fraction.

The denominator will distribute, allowing us to address each element separately.

Now we can cancel common factors to find our answer.

Divide the leading coefficients to get the first term of the quotient:

, the first term of the quotient

Multiply this term by the divisor, and subtract the product from the dividend:

Repeat these steps with the differences until the difference is an integer. As it turns out, we need to repeat only once:

, the second term of the quotient

, the remainder

Putting it all together, the quotient can be written as .

This is not a FOIL problem, as we are adding rather than multiplying the terms in parenteses.

Add like terms to solve.

Combining these terms into an expression gives us our answer.

The polynominal breaks down to , and once you factor out a from the denomintator and cancel, you are left with .

First, rewrite this problem so that the missing term is replaced by

Divide the leading coefficients:

, the first term of the quotient

Multiply this term by the divisor, and subtract the product from the dividend:

Repeat this process with each difference:

, the second term of the quotient

One more time:

, the third term of the quotient

, the remainder

The quotient is and the remainder is ; this can be rewritten as a quotient of

Set up this problem vertically like you would a normal multiplication problem without variables. Then, multiply the term to each term in the trinomial. Next, multiply the term to each term in the trinomial (keep in mind your placeholder!).

Then combine the two, which yields:

It is important to remember that ;

It is easiest to break this problem into groups, group the constant terms together, then group the N variables and group the P variables, like so.

Then reduce each fraction