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The square rules

The square rules are shortcuts for expanding common parenthesised expressions, and are used in reverse when factoring. They show up everywhere when simplifying algebraic expressions.

(a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2first square rule
(a−b)2=a2−2ab+b2(a-b)^2 = a^2 - 2ab + b^2second square rule
(a+b)(a−b)=a2−b2(a+b)(a-b) = a^2 - b^2difference of squares

Symbols

a, ba,\ bterms in the parentheses

Example

(x+3)2=x2+6x+9(x+3)^2 = x^2 + 6x + 9.

(x+3)(x−3)=x2−9(x+3)(x-3) = x^2 - 9.

(a+b)2≠a2+b2(a+b)^2 \neq a^2 + b^2 - the middle term 2ab2ab is often forgotten.
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Part of Foundations of Mathematics: Algebra and equations.