Square Algebraic Identities

An algebraic identity is an equation that is true for all allowed values of the variables.

Square identities help students expand and simplify expressions quickly.

They are used in mental maths, factorisation, quadratics, and algebraic proofs.

An identity is different from an ordinary equation. It is true for every value that can be used.

Square identities come from multiplying binomials.

$(a + b)^2$ means ($a + b$)($a + b$), not $a^{2} + b^{2}$.

$(a - b)^2$ means ($a - b$)($a - b$), so the middle term is negative.

The difference of squares identity works when two square terms are separated by subtraction.

You will learn

• Understand what an identity means.
• Use $(a + b)^2$.
• Use $(a - b)^2$.
• Use $a^{2} - b^{2}$.
• Apply identities to numbers and algebraic expressions.