# Polynomials

### Contents

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#### Square of a Binomial

To square a binomial, multiply the binomial by itself:
(a + b)2 = (a + b)(a + b)

 (a + b)2 = (a + b)(a + b) = a 2 + ab + ba + b 2 = a 2 + ab + ab + b 2 = a 2 +2ab + b 2

The square of a binomial is always the sum of:

1. The first term squared,
2. 2 times the product of the first and second terms, and
3. the second term squared.

When a binomial is squared, the resulting trinomial is called a perfect square trinomial.

Examples:

(x + 5)2 = x 2 +2(x)(5) + 52 = x 2 + 10x + 25
(100 - 1)2 = 1002 +2(100)(- 1) + (- 1)2 = 10000 - 200 + 1 = 9801
(2x - 3y)2 = (2x)2 +2(2x)(- 3y) + (- 3y)2 = 4x 2 -12xy + 9y 2

#### Product of the Sum and Difference of Two Terms

When we multiply two polynomials that are the sum and difference of the same 2 terms -- (x + 5) and (x - 5) for example -- we get an interesting result:

 (a + b)(a - b) = a(a) + a(- b) + ba + b(- b) = a 2 - ab + ab - b 2 = a 2 - b 2

The product of the sum and difference of the same two terms is always the difference of two squares; it is the first term squared minus the second term squared. Thus, this resulting binomial is called a difference of squares.

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