This is a difference of squares. The difference of squares formula is _a_2 – _b_2 = (a + b)(a – b).

In this problem, a = 6_x_ and b = 7_y_:

36_x_2 – 49_y_2 = (6_x_ + 7_y_)(6_x_ – 7_y_)

This can be solved by looking at all of the answers and multiplying them and comparing to the answer. However this is time consuming. You can start by noting that the term can be a result of , where one of the terms is negative, so one answer can be eliminated. It is also clear that must be the result of multiplied by , so two additional answers can be eliminated. Looking at the last two answers and multiplying through, the correct answer can be determined.

Because the term has a coefficient, you begin by multiplying the and the terms () together: .

Find the factors of that when added together equal the second coefficient (the term) of the polynomial: .

There are four factors of : , and only two of those factors, , can be manipulated to equal when added together and manipulated to equal when multiplied together:

Begin by separating into like terms. You do this by multiplying and , then finding factors which sum to

Now, extract like terms:

Simplify:

Factor:

When factoring a polynomial , the product of the coefficients must be , the sum of the factors must be , and the product of the factors must be .

For the above equation, , , and .

Set up the factor equation:

Becauase is negative, one of the factors must be negative as well. Because is positive, this means the larger factor is positive as well.

Two numbers that meet these requirements are and . Their product is , and their sum is .

To begin, distribute the squares:

Now, combine like terms:

The common factor here is . Pull this out of both terms to simplify:

Before we do anything, we notice that both terms in the expression have a common factor of 4. Thus, we can factor it out, leaving us with: . We recognize that the expression inside the parentheses is a difference of squares, and factors as such: . Finally, we are done.

Here you have an expression with three variables. To factor, you will need to pull out the greatest common factor that each term has in common.

Only the last two terms have so it will not be factored out. Each term has at least and so both of those can be factored out, outside of the parentheses. You'll fill in each term inside the parentheses with what the greatest common factor needs to be multiplied by to get the original term from the original polynomial:

Use the difference of perfect cubes equation:

In ,

and