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}

2 - u^{2} + - u^{4} + - u^{6}

(4 l - 2 m)^{3}

\frac{( d ^{\frac{1}{2}} \cdot e ^{x} )}{( d \cdot x ^{\frac{1}{2}} )}

4 x - 24

\frac{( 3 x ^{2} + 5 x + 2 )}{x + 1}

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