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We know that:
a(b + c) = ab + ac
The reverse process, ab + ac = a(b + c),
is called taking out the common factor.
Consider the factorisation of the expression 5x + 15.
Note that the common factor 5 has been taken out and placed in front of
the brackets. The expression inside the brackets is obtained by
dividing each term by 5.
In general:
To factorise an algebraic expression, take out the
highest common
factor and place it in front of the brackets. Then the expression
inside the brackets is obtained by dividing each term by the highest
common factor.
Example 25
Factorise the following:
Solution:
Alternative way:
Often, we set out the solution as follows:
Note:
The process of taking out a common factor is of great importance in
algebra. With practice you will be able to find the highest common
factor (HCF) readily and hence factorise the given
expression.
Example 26
Factorise the following:
Solution:
Note:
We can check the answer by using the Distributive Law.
Key Terms
taking out a common factor
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