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Algebraic expressions - AQAFactorising

Letters can be used to stand for unknown values or values that can change. Formulas can be written and equations solved in a range of problems in science and engineering.

Part of MathsAlgebra

Factorising

Factorising is the reverse process of expanding brackets. A factorised answer will always contain a set of brackets.

To factorise an expression fully, take out the of all the terms. For example, \(2x\) is the HCF of \(4x^2\) and \(6x\) as 2 is the biggest number that will divide into 4 and 6 and \(x\) is the biggest variable that will divide into \(x^2\) and \(x\).

Example

Factorise \(6x + 9\).

To factorise this expression, look for the HCF of \(6x\)and 9 which is 3. To factorise, write down the HCF and then begin a set of brackets. Find the missing terms in the brackets by dividing each of the terms given in the question by the HCF.

The HCF of \(6x + 9\) is 3. Put this outside the bracket:

\(3(? + ?)\)

Find the missing terms in the bracket by dividing each term by the HCF:

\(6x \div 3 = 2x\) and \(9 \div 3 = 3\)

This gives: \(3(2x + 3)\)

To check this answer is correct, expand the bracket and check that the answer matches the original equation:

\(3(2x + 3) = 3 \times 2x + 3 \times = 6x + 9\)

Question

Factorise \(12ab - 8ac + 4a^2b\).

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