Expansion & Factorisation

What you'll learn

Expanding brackets with the special identities, factorising quadratic expressions, and simplifying algebraic fractions.

• Squaring a sum: \((a+b)^2 = a^2 + 2ab + b^2\)
• Squaring a difference: \((a-b)^2 = a^2 - 2ab + b^2\)
• Difference of two squares: \(a^2 - b^2 = (a+b)(a-b)\)
• Factorising \(x^2 + bx + c\): find two numbers that multiply to \(c\) and add to \(b\)
• Factorising a non-monic quadratic \(ax^2+bx+c\) (\(a \neq 1\))
• Simplifying an algebraic fraction means factorising first, then cancelling