# What are the special products of polynomials?

## What are the special products of polynomials?

One characteristic of special products is that the first and last terms of these polynomials are always perfect squares (a2 and b2). If the first and last terms of a polynomial are perfect squares, the polynomial could be the result of a special product.

## What are the special cases for multiplying polynomials?

Special Cases of Polynomials

• Square a binomial.
• Find a difference of squares.
• Perform operations on polynomials with several variables.

## What is the special product pattern?

There are a couple of special instances where there are easier ways to find the product of two binominals than multiplying each term in the first binomial with all terms in the second binomial. This is a pattern that’s called the square of a binomial pattern.

## What is the special product rule?

In other words, when you have a binomial squared, you end up with the first term squared plus (or minus) twice the product of the two terms plus the last term squared. Any time you have a binomial squared you can use this shortcut method to find your product. This is a special products rule.

## What are the 5 special products?

Special Products involving Squares

• a(x + y) = ax + ay (Distributive Law)
• (x + y)(x − y) = x2 − y2 (Difference of 2 squares)
• (x + y)2 = x2 + 2xy + y2 (Square of a sum)
• (x − y)2 = x2 − 2xy + y2 (Square of a difference)

## What are the types of special products?

Special products of binomials

• Special products of the form (x+a)(x-a) Squaring binomials of the form (x+a)² Practice: Multiply difference of squares. Special products of the form (ax+b)(ax-b) Squaring binomials of the form (ax+b)² Special products of binomials: two variables.
• Multiplying binomials by polynomials.

## How many special products are there?

Special products are simply special cases of multiplying certain types of binomials together. We have three special products: (a + b)(a + b) (a – b)(a – b)

## What is the example of special product?

Another special binomial product is the product of a sum and a difference of terms. For example, let’s multiply the following binomials. When multiplying a sum and difference of the same two terms, the middle terms cancel out. We get the square of the first term minus the square of the second term.

## How do you identify a special product?

You identify special products by their values if its a perfect square or cubes..

## What is the formula for special products?

In mathematics, special products are of the form: (a+b)(a-b) = a2 – b2 (Product of sum and difference of two terms) which can be used to quickly solve multiplication such as:

## How do special products help us factor polynomials?

Special products make it easier to factor polynomials as certain special patterns are formed when a polynomial has a specific group of factors. For example, if a polynomial has the form a^2 – b^2…

## What are the different ways to factor polynomials?

To factor the polynomial. for example, follow these steps: Break down every term into prime factors. This expands the expression to. Look for factors that appear in every single term to determine the GCF. In this example, you can see one 2 and two x’s in every term. These are underlined in the following:

## What is a factor polynomial?

Factorization of a Polynomial. A factor of polynomial P(x) is any polynomial which divides evenly into P(x). For example, x + 2 is a factor of the polynomial x 2 – 4. The factorization of a polynomial is its representation as a product its factors. For example, the factorization of x 2 – 4 is (x – 2)(x + 2).