2.1  Expansion
  Expansion of algebraic expression is the product of multiplication
of one or two expressions in brackets.
Expansion on Two Algebraic Expressions
  • When doing an expansion of algebraic expressions, every term within the bracket needs to be multiplied with the term outside the bracket.
  \(\begin{aligned} a(x+y) &=(a\times x)+(a\times y) \\\\&= ax +ay. \end{aligned}\)  
  Combined Operations including Expansion
  • Combine operations for algebraic terms must be solved by following the 'BODMAS' rule.
  \(\begin{aligned} \\\text{B} &= \text{Brackets} \\\\ \text{O} &= \text{Order} \\\\ \text{D} &= \text{Division} \\\\ \text{M} &= \text{Multiplication} \\\\ \text{A} &= \text{Addition} \\\\ \text{S} &= \text{Subtraction} \end{aligned}\)
  (i) \(\begin{aligned} &\space(m+n)(x+y) \\\\&= mx +my +nx +ny. \end{aligned}\)
  (ii) \(y(x+z) = yx + yz\)
  (iii) \(\begin{aligned} &\space(b+c)(d+e)\\\\&= bd +be + cd + ce. \end{aligned}\)
  (iv) \(\begin{aligned} &\space(d+e)^2 \\\\&=(d+e)(d+e) \\\\&=d^2+de+de+e^2 \\\\&= d^2 + 2 de + e^2. \end{aligned}\)
  (v) \(\begin{aligned} &\space(k-l)^2 \\\\&=(k-l)(k-l) \\\\&=k^2-kl-kl+l^2 \\\\&= k^2 -2kl + l^2. \end{aligned}\)
  (vi) \((b+c)(b-c) = b^2 -c^2\)
  (vii) \(\begin{aligned} &(h-j)^2-2h(3h-3j) \\\\&=(h-j)(h-j)-6h^2+6hj \\\\&=h^2-2hj+j^2-6h^2+6hj \\\\&=-5h^2+j^2+4hj. \end{aligned}\)