Factorising
Year 8 📊 Algebra Factorise expressions by taking out common factors.
🔍 Common Factor Factorising
Factorising is the reverse of expanding. Find the highest common factor (HCF) of all terms and take it outside a bracket.
- Find the HCF of all the coefficients.
- Find any variables common to all terms.
- Write the HCF outside and divide each term by it inside the bracket.
Example: Factorise $6x^2 + 9x$ → HCF is $3x$ → $3x(2x + 3)$
🔲 Factorising Quadratics ($a = 1$)
A quadratic $x^2 + bx + c$ can often be factorised into two brackets $(x+p)(x+q)$.
⚡ Find $p$ and $q$ such that
$$p + q = b \quad \text{and} \quad p \times q = c$$Example: Factorise $x^2 + 5x + 6$ → need numbers adding to 5 and multiplying to 6: 2 and 3 → $(x+2)(x+3)$
Example: Factorise $x^2 - x - 12$ → numbers adding to -1, multiplying to -12: 3 and -4 → $(x+3)(x-4)$
⭐ Difference of Two Squares
Recognise the special pattern $a^2 - b^2 = (a+b)(a-b)$ and apply it immediately.
Example: Factorise $x^2 - 25 = (x+5)(x-5)$
Example: Factorise $4x^2 - 9 = (2x+3)(2x-3)$
Always check for a common factor first, before trying other methods.
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