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Factorise completely $x - 4x^2$ - Edexcel - A-Level Maths Pure - Question 3 - 2013 - Paper 3

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Factorise completely $x - 4x^2$

Worked Solution & Example Answer:Factorise completely $x - 4x^2$ - Edexcel - A-Level Maths Pure - Question 3 - 2013 - Paper 3

Step 1

Take out a common factor

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Answer

We start by taking out a common factor of xx: x(1−4x)x(1 - 4x)

Step 2

Factor the quadratic expression

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Answer

Next, we recognize that 1−4x1 - 4x is a quadratic expression. This can be factored further as follows: 1−4x=1−(2x)2=(1−2x)(1+2x)1 - 4x = 1 - (2x)^2 = (1 - 2x)(1 + 2x)

Step 3

Combine the factors

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Answer

Thus, combining all the factors, the complete factorization of the original expression is: x(1−2x)(1+2x)x(1 - 2x)(1 + 2x)

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