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Factorise fully 25x - 9x³. - Edexcel - A-Level Maths Pure - Question 3 - 2014 - Paper 2

Question 3

Factorise fully 25x - 9x³.

Worked Solution & Example Answer:Factorise fully 25x - 9x³. - Edexcel - A-Level Maths Pure - Question 3 - 2014 - Paper 2

Step 1

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Answer

To begin the factorization process, we can factor out the common term x from the expression. By doing this, we get:

$x(25 - 9x^2)$

This step is crucial as it simplifies our expression and prepares it for further factorization.

Step 2

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Answer

Next, we recognize that the term (25 - 9x²) is a difference of squares. This can be expressed as:

$(5 - 3x)(5 + 3x)$

Therefore, the expression can be further factorized as:

$x(5 - 3x)(5 + 3x)$

This highlights the complete factorization of the original expression.

Step 3

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101 rated

Answer

The final expression, fully factored, is:

$x(5 - 3x)(5 + 3x)$

This shows that the expression consists of three distinct factors, as required.

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