What is factor a^2+2a(a+b)+(a+b)^2 ?

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

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factor a^2+2a(a+b)+(a+b)^2

factor

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

(2 a + b)^{2}

Solution steps

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

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

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

Expand

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

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

Simplify

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

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

Rewrite

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

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

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

Apply Perfect Square Formula:

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

a = 2 a, b = b

= (2 a + b)^{2}

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What is factor a^2+2a(a+b)+(a+b)^2 ?
The solution to factor a^2+2a(a+b)+(a+b)^2 is (2a+b)^2