How do you factor a special binomial?

We use this formula to factor certain special binomials.

1. Example 1: Factor: x2−16 x 2 − 16 .
2. Solution:
3. Step 1: Identify the binomial as difference of squares and determine the square factors of each term.
4. Step 2: Substitute into the difference of squares formula.
5. Step 3: Multiply to check.

What is special factoring?

When we learned how to multiply polynomials, we learned how to quickly multiply commonly occurring scenarios using “special products” formulas. When we reverse these formulas, we end up with the factored form, this is referred to as “special factoring”.

What is special products of binomials?

Some special products of binomials suggest other patterns, such as the product of the sum and difference of two expressions, the product of squaring the sum of an expression, and the product of squaring the difference of an expression.

Which is the formula for factoring special binomials?

Solution: Here we have a binomial with two variables and recognize that it is a difference of squares. Therefore, a = 7x and b = 10y. Substitute into the formula for difference of squares. Try this! Factor: 36×2 − 1. Given any real number b, a polynomial of the form x2 + b2 is prime. Furthermore, the sum of squares

Can A trinomial be factored using special products?

If you learn to recognize these kinds of polynomials, you can use the special products patterns to factor them much more quickly. Some trinomials are perfect squares. They result from multiplying a binomial times itself. You can square a binomial by using FOIL, but using the Binomial Squares pattern you saw in a previous chapter saves you a step.

Are there any special factor patterns in Algebra?

Here are the special factor patterns you should be able to recognize. Memorize the formulas, because in some cases, it’s very hard to generate them without wasting a lot of time. A perfect square is a quantity that results when something is multiplied by itself, and a perfect cube is the result of multiplying something by itself twice.

How are binomials related to Special Products in Algebra?

We have seen that some binomials and trinomials result from special products—squaring binomials and multiplying conjugates. If you learn to recognize these kinds of polynomials, you can use the special products patterns to factor them much more quickly.