What is (a+b+c)^2+(a-b-c)^2 ?

The solution to (a+b+c)^2+(a-b-c)^2 is 2a^2+2b^2+4bc+2c^2

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simplify (a+b+c)^2+(a-b-c)^2

simplify

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

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

Solution steps

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

a^{2} + a^{2} = 2 a^{2}

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

Add similar elements:

2 ab - 2 ab = 0

= 2 a^{2} + 2 a c - 2 a c + b^{2} + b^{2} + 2 b c + 2 b c + c^{2} + c^{2}

Add similar elements:

2 a c - 2 a c = 0

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

Add similar elements:

b^{2} + b^{2} = 2 b^{2}

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

Add similar elements:

2 b c + 2 b c = 4 b c

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

Add similar elements:

c^{2} + c^{2} = 2 c^{2}

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

\frac{( 8 ^{\frac{1}{3}} \times 1 6 ^{\frac{1}{3}} )}{3 2 ^{- 1}} /3

\frac{( 10 x ^{2} + 19 x + 6 )}{( 2 x + 3 )}

\frac{( x - 5 + 10 )}{( x + 5 - x )}

8 x^{3} y - 32 x^{2} y + 32 x y

x^{4} + 31 x^{2} y^{2} + 400 y^{4}

What is (a+b+c)^2+(a-b-c)^2 ?
The solution to (a+b+c)^2+(a-b-c)^2 is 2a^2+2b^2+4bc+2c^2