What is Factorisation?
Factorisation refers to the process of expressing an algebraic expression as a product of its factors. Factors can be numerical values, algebraic variables, or entire algebraic expressions themselves. Some expressions are already in their factor form like 3xy or 5(x+1)(x+2), while others, such as 2x + 4, require techniques to identify their factors.
Key Techniques of Factorisation:
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Method of Common Factors: This involves identifying the highest common factor (HCF) in terms of numerical coefficients and algebraic variables and then factoring it out of the expression.
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Regrouping Terms: In some cases, it's beneficial to rearrange or regroup the terms in an expression to isolate common factors. This method allows us to factor expressions that do not have an obvious common factor across all terms.
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Using Identities: Familiarity with algebraic identities, such as
- (a + b)² = a² + 2ab + b²
- (a - b)² = a² - 2ab + b²
- a² - b² = (a + b)(a - b)
can facilitate the factorisation of expressions fitting these forms.
We also discuss more complicated expressions like quadratics and polynomials, illustrating methods to factor them systematically. Through practice and exercises, learners gain familiarity with these techniques, essential for solving various algebraic problems.
Similar Question:
Example 2: Factorise
\[ 18ac + 24a^2c^2 \]
Solution:
We have
\[ 18ac = 2 \times 3 \times 3 \times a \times c \]
\[ 24a^2c^2 = 2 \times 2 \times 2 \times 3 \times a \times a \times c \times c \]
The two terms have \( 6ac \) as a common factor.
Therefore,
\[ 18ac + 24a^2c^2 = 6ac \left( 3 + 4ac \right) \]
\[ = 6ac(3 + 4ac) \quad (\text{required factor form}) \]