Editing Difference of two squares (section)

===Factorization of polynomials and simplification of expressions===
The formula for the difference of two squares can be used for factoring [[polynomial]]s that contain the square of a first quantity minus the square of a second quantity. For example, the polynomial <math>x^4 - 1</math> can be factored as follows:

<math display=block>x^4 - 1 = (x^2 + 1)(x^2 - 1) = (x^2 + 1)(x + 1)(x - 1).</math>

As a second example, the first two terms of <math>x^2 - y^2 + x - y</math> can be factored as <math>(x + y)(x - y)</math>, so we have:
<math display=block>
x^2 - y^2 + x - y = (x + y)(x - y) + x - y = (x - y)(x + y + 1).
</math>
Moreover, this formula can also be used for simplifying expressions:
<math display=block>
(a+b)^2-(a-b)^2=(a+b+a-b)(a+b-a+b)=(2a)(2b)=4ab.
</math>