Factorisation

Example 13: Factorize

1. Substitution:

Observe that

appears in both terms. Let

Substituting

into the expression:

2. Factorizing the Quadratic in

To factorize

, we look for two numbers that multiply to

and add up to

(the coefficient of

). These numbers are

and

3. Substituting back for

Replace

with

again:

4. Further Factorization:

Now, factorize each of the two quadratic expressions separately:

Part 1:

Splitting the middle term:

and

Part 2:

This is a perfect square:

Final Answer:

Putting it all together, the completely factorized form is:

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