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Factorise completely $$x^3 - 9x$$. - Edexcel - A-Level Maths Pure - Question 4 - 2008 - Paper 1

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Factorise completely $$x^3 - 9x$$.

Worked Solution & Example Answer:Factorise completely $$x^3 - 9x$$. - Edexcel - A-Level Maths Pure - Question 4 - 2008 - Paper 1

Step 1

First factor out the common term

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Answer

To begin factoring the expression, we can factor out the common term, which is xx:

x(x2−9)x(x^2 - 9).

Step 2

Recognize the difference of squares

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Answer

The expression x2−9x^2 - 9 is a difference of squares, which can be factored further:

x2−9=(x−3)(x+3)x^2 - 9 = (x - 3)(x + 3).

Step 3

Combine factors for final answer

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Answer

Combining the factored terms gives us the fully factored expression:

x(x−3)(x+3)x(x - 3)(x + 3).

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