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

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

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

simplify

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

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

Solution steps

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

Expand

- 2 (b - c)^{2} : - 2 b^{2} + 4 b c - 2 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} - 2 b^{2} + 4 b c - 2 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^{2} - 2 b c + 2 b c + 4 b c + c^{2} - c^{2} - 2 c^{2}

Add similar elements:

a^{2} - a^{2} = 0

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

Add similar elements:

2 ab + 2 ab = 4 ab

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

Add similar elements:

- 2 a c - 2 a c = - 4 a c

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

Add similar elements:

b^{2} - b^{2} - 2 b^{2} = - 2 b^{2}

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

Add similar elements:

- 2 b c + 2 b c + 4 b c = 4 b c

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

Add similar elements:

c^{2} - c^{2} - 2 c^{2} = - 2 c^{2}

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

(2 s + 1) (2 s + 9) - (2 s)^{2}

2 \frac{x}{3} - 3 \frac{x}{8} - \frac{7}{12}

\frac{( 10 x ^{3} \cdot y ^{5} )}{( 2 x ^{2} \cdot y )}

- \frac{11}{a} \cdot \frac{b}{3}

- 4 x y^{3} (5 x^{2} + 8 y)

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