## Factorisation

2.2  Factorisation

 Definition A process of determining the factors of an algebraic expression or algebraic terms and when multiplied together will form the original expressions. Also known as the reverse process of expansion.

Terms that related to the Product of Algebraic Expressions

(i)

Factor

• A number or quantity that when multiplied with another produces a given number or expression.

(ii)

Common factor

• The factor of an algebra term that divides two or more other terms exactly.

(iii)

Highest Common Factor (HCF)

• The largest of those common factors.

Factorisation of Algebraic Expressions

(i)

Using HCF

 Example Factorise $$7x +35$$. \begin{aligned} \space 7x &= 7 \times x \\\\ 35 &= 5 \times 7 \\\\ \therefore \text{HCF} &= 7.\\\\ \end{aligned} The algebraic expressions, $$7x +35$$ can be written as a product of two factors, $$7(x +5)$$.

The common factor, $$7$$, has been taken out and placed in front of the bracket.

The expression inside the bracket is obtained by dividing each term with $$7$$.

(ii)

Using difference of squares of two terms

• This method can only be used if the two algebraic terms are perfect squares.

(iii)

Using Cross Multiplication

• Algebraic expressions of $$ax^2 + bx + c ,$$ where by $$a \neq0$$ and $$a,b,c$$ are integers that can be factorised.

(iv)

Using common factors involving $$4$$ algebraic terms

 Example \begin{aligned} &\space jm-jn+ym-yn\\\\& = j(m-n) + y(m-n) \\\\& = (j+y)(m-n). \end{aligned}