Factor 4x^2+4x+1

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Algebra

Factor 4x^2+4x+1

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

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

${(2 x)}^{2} + 4 x + 1$

Rewrite $1$ as $1^{2}$ .

${(2 x)}^{2} + 4 x + 1^{2}$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 x = 2 \cdot (2 x) \cdot 1$

Rewrite the polynomial.

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

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 2 x$ and $b = 1$ .

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

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