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G S Rehill's Interactive Maths Software Series - "Building a Strong Foundation in Mathematics" from mathsteacher.com.au.

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Year 10 Interactive Maths - Second Edition


Use of Substitution

Substitution is used to convert an expression into a more familiar form.


Example 13

Factorise (factorize) 4(x+1)^2 + 8(x+1) + 3.

Solution:

Substitute a=x+1 and factorise 4a^2+8a+3.

Find the factors of the first term and factors of the last term.

The factors 4a and a do not lead to the middle term.

Now try the factors 2a and 2a.

The linear factors (2a+1) and (2a+3) lead to the middle term 8a.

So 4a^2+8a+3=(2a+1)(2a+3).

Substitute a=x+1 to find the factorisation is (2x+3)(2x+5).

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