What is factor m^2+2m(m+n)+(m+n)^2 ?

The solution to factor m^2+2m(m+n)+(m+n)^2 is (2m+n)^2

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factor m^2+2m(m+n)+(m+n)^2

factor

m^{2} + 2 m (m + n) + (m + n)^{2}

(2 m + n)^{2}

Solution steps

m^{2} + 2 m (m + n) + (m + n)^{2}

(m + n)^{2} : m^{2} + 2 mn + n^{2}

= m^{2} + 2 m (m + n) + m^{2} + 2 mn + n^{2}

Expand

2 m (m + n) : 2 m^{2} + 2 mn

= m^{2} + 2 m^{2} + 2 mn + m^{2} + 2 mn + n^{2}

Simplify

m^{2} + 2 m^{2} + 2 mn + m^{2} + 2 mn + n^{2} : 4 m^{2} + 4 mn + n^{2}

= 4 m^{2} + 4 mn + n^{2}

Rewrite

4 m^{2} + 4 mn + n^{2}

(2 m)^{2} + 2 \cdot 2 mn + n^{2}

= (2 m)^{2} + 2 \cdot 2 mn + n^{2}

Apply Perfect Square Formula:

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

a = 2 m, b = n

= (2 m + n)^{2}

2.25 x^{2} - 3 x + 1

x^{2} - 4 + 4

x - 10 x y + 25 y

y^{2} - 19 + 51

x (a x - 1) (a x - 1) (x + 1) + a

What is factor m^2+2m(m+n)+(m+n)^2 ?
The solution to factor m^2+2m(m+n)+(m+n)^2 is (2m+n)^2