How do you factor $4 x^{2} + 4 x + 1$ $4x^2+4x+1$ ?

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How do you factor $4 x^{2} + 4 x + 1$ $4x^2+4x+1$ ?

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Answer 1 · 2017-05-13T11:01:35

${(2 x + 1)}^{2}$ $(2x+1)^2$

Explanation:

$'split 4x into 2 x + 2 x$ $"'split 4x into " 2x+2x$

$\Rightarrow 4 x^{2} + 2 x + 2 x + 1$ $rArr4x^2+2x+2x+1$

$factorise each 'pair'$ $"factorise each 'pair'""$

$2 x (2 x + 1) + 1 (2 x + 1)$ $color(red)(2x)(2x+1)color(red)(+1)(2x+1)$

$take out the common factor (2 x + 1)$ $"take out the common factor " (2x+1)$

$(2 x + 1) (2 x + 1)$ $(2x+1)(color(red)(2x+1))$

$\Rightarrow 4 x^{2} + 4 x + 1$ $rArr4x^2+4x+1$

$= (2 x + 1) (2 x + 1) = {(2 x + 1)}^{2}$ $=(2x+1)(2x+1)=(2x+1)^2$

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How do you factor $4 x^{2} + 4 x + 1$ $4x^2+4x+1$ ?

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