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Factorisation Using Algebraic Identities

Factorise: ...

Question

Factorise: $4 x^{2} + 4 x + 1$

A

(4 x + 1) (4 x + 1)

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B

(2 x - 1) (2 x + 1)

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C

(2 x + 1) (2 x + 1)

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D

(4 x - 1) (4 x + 1)

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Solution

The correct option is C $(2 x + 1) (2 x + 1)$
$4 x^{2} + 4 x + 1$
Now splitting the middle term,
$= 4 x^{2} + 2 x + 2 x + 1$
$= 2 x (2 x + 1) + 1 (2 x + 1)$
$= (2 x + 1) (2 x + 1)$
Therefore, $4 x^{2} + 4 x + 1 = (2 x + 1) (2 x + 1)$

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