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Expansion
Expansion
2.1
Expansion
Definition
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.
Example
\(\begin{aligned} a(x+y) &=(a\times x)+(a\times y) \\\\&= ax +ay. \end{aligned}\)
Combined Operations including Expansion
Combine operations for algebraic terms must be solved by following the 'BODMAS' rule.
\(\begin{aligned} \\\text{B} &= \text{Brackets} \\\\ \text{O} &= \text{Order} \\\\ \text{D} &= \text{Division} \\\\ \text{M} &= \text{Multiplication} \\\\ \text{A} &= \text{Addition} \\\\ \text{S} &= \text{Subtraction} \end{aligned}\)
Examples
(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)
\(\begin{aligned} &(h-j)^2-2h(3h-3j) \\\\&=(h-j)(h-j)-6h^2+6hj \\\\&=h^2-2hj+j^2-6h^2+6hj \\\\&=-5h^2+j^2+4hj. \end{aligned}\)
Expansion
2.1
Expansion
Definition
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.
Example
\(\begin{aligned} a(x+y) &=(a\times x)+(a\times y) \\\\&= ax +ay. \end{aligned}\)
Combined Operations including Expansion
Combine operations for algebraic terms must be solved by following the 'BODMAS' rule.
\(\begin{aligned} \\\text{B} &= \text{Brackets} \\\\ \text{O} &= \text{Order} \\\\ \text{D} &= \text{Division} \\\\ \text{M} &= \text{Multiplication} \\\\ \text{A} &= \text{Addition} \\\\ \text{S} &= \text{Subtraction} \end{aligned}\)
Examples
(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)
\(\begin{aligned} &(h-j)^2-2h(3h-3j) \\\\&=(h-j)(h-j)-6h^2+6hj \\\\&=h^2-2hj+j^2-6h^2+6hj \\\\&=-5h^2+j^2+4hj. \end{aligned}\)
Chapter : Factorisation and Algebraic Fractions
Topic : Expansion
Form 2
Mathematics
View all notes for Mathematics Form 2
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