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Factorising expressions

Factorisation is the opposite of expansion. Factorisation involves finding the common factors of an expression and rewriting it as the product of simpler expressions.

The expression on the right is the factorisation of the expression on the left.

$$$ x^2 + x -2 = (x-1)(x+2)$$$

To fully factorise an expression, you need to identify all the common factors. There is no overall rule.

$$$ 3y+6 = \Tgreen{3}\times y + \Tgreen{3}\times 2 = \Tgreen{3}(y+2)$$$ $$$ 2a^2 -4a = \Tgreen{2a}\times a - \Tgreen{2a}\times 2 = \Tgreen{2a}(a-2)$$$

Factorisation is very useful when you need to find the solutions to an equation!