What is factor a^2+4ab+4b^2 ?

The solution to factor a^2+4ab+4b^2 is (a+2b)^2

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factor a^2+4ab+4b^2

factor

a^{2} + 4 ab + 4 b^{2}

(a + 2 b)^{2}

Solution steps

a^{2} + 4 ab + 4 b^{2}

Rewrite in the form of

a^{2} + 2 ab + b^{2} :

4 b^{2} = (2 b)^{2}

4 ab = 2 a \cdot 2 b

= a^{2} + 2 a \cdot 2 b + (2 b)^{2}

Apply Perfect Square Formula:

a^{2} + 2 ab + b^{2} = (a + b)^{2}

a^{2} + 2 a \cdot 2 b + (2 b)^{2} = (a + 2 b)^{2}

= (a + 2 b)^{2}

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