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.

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

Expansion

Chapter : Factorisation and Algebraic Fractions

Topic : Expansion

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