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The square identities

The square identities are three rules that make it quick to expand and factorise expressions. The first and second give the square of a sum and of a difference, and the difference of squares gives the product of a sum and a difference. Used backwards they help when factorising or simplifying fractions.

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

square of a sum

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

square of a difference

(a + b)(a - b) = a^2 - b^2

difference of squares

Symbols

a,\ b

numbers or expressions

Example

$(x + 3)^2 = x^2 + 6x + 9$ . Check with $x = 2$ : $(2 + 3)^2 = 25$ and $4 + 12 + 9 = 25$ .

The most common mistake is forgetting the middle term

2ab

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Part of Mathematics 1T: Algebra and equations.