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

The solution to (2a+2b-c)^2+(2b+2c-a)^2b+(2c+2a-b)^2 is 8a^2+4ab+4ac+5b^2-8bc+5c^2+b(2b+2c-a)^2

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

simplify

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

8 a^{2} + 4 ab + 4 a c + 5 b^{2} - 8 b c + 5 c^{2} + b (2 b + 2 c - a)^{2}

Solution steps

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

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

Expand

(2 a + 2 b - c)^{2} : 4 a^{2} + 8 ab - 4 a c + 4 b^{2} - 4 b c + c^{2}

= 4 a^{2} + 8 ab - 4 a c + 4 b^{2} - 4 b c + c^{2} + b (2 b + 2 c - a)^{2} + (2 c + 2 a - b)^{2}

Expand

(2 c + 2 a - b)^{2} : 4 c^{2} + 4 a^{2} + 8 a c - 4 b c - 4 ab + b^{2}

= 4 a^{2} + 8 ab - 4 a c + 4 b^{2} - 4 b c + c^{2} + b (2 b + 2 c - a)^{2} + 4 c^{2} + 4 a^{2} + 8 a c - 4 b c - 4 ab + b^{2}

Group like terms

= 4 a^{2} + 4 a^{2} + 8 ab - 4 ab - 4 a c + 8 a c + 4 b^{2} + b^{2} - 4 b c - 4 b c + c^{2} + 4 c^{2} + b (2 b + 2 c - a)^{2}

Add similar elements:

4 a^{2} + 4 a^{2} = 8 a^{2}

= 8 a^{2} + 8 ab - 4 ab - 4 a c + 8 a c + 4 b^{2} + b^{2} - 4 b c - 4 b c + c^{2} + 4 c^{2} + b (2 b + 2 c - a)^{2}

Add similar elements:

8 ab - 4 ab = 4 ab

= 8 a^{2} + 4 ab - 4 a c + 8 a c + 4 b^{2} + b^{2} - 4 b c - 4 b c + c^{2} + 4 c^{2} + b (2 b + 2 c - a)^{2}

Add similar elements:

- 4 a c + 8 a c = 4 a c

= 8 a^{2} + 4 ab + 4 a c + 4 b^{2} + b^{2} - 4 b c - 4 b c + c^{2} + 4 c^{2} + b (2 b + 2 c - a)^{2}

Add similar elements:

4 b^{2} + b^{2} = 5 b^{2}

= 8 a^{2} + 4 ab + 4 a c + 5 b^{2} - 4 b c - 4 b c + c^{2} + 4 c^{2} + b (2 b + 2 c - a)^{2}

Add similar elements:

- 4 b c - 4 b c = - 8 b c

= 8 a^{2} + 4 ab + 4 a c + 5 b^{2} - 8 b c + c^{2} + 4 c^{2} + b (2 b + 2 c - a)^{2}

Add similar elements:

c^{2} + 4 c^{2} = 5 c^{2}

= 8 a^{2} + 4 ab + 4 a c + 5 b^{2} - 8 b c + 5 c^{2} + b (2 b + 2 c - a)^{2}

33 \cdot x^{3} - 22 \cdot y^{3}

\frac{( 3 x - 1 )}{( 3 - x )}

25 y^{2} - 16 z^{2}

(8 x)^{7} (8 x)^{- 6}

2^{k} + 2^{k} \cdot 2^{1}

What is (2a+2b-c)^2+(2b+2c-a)^2b+(2c+2a-b)^2 ?
The solution to (2a+2b-c)^2+(2b+2c-a)^2b+(2c+2a-b)^2 is 8a^2+4ab+4ac+5b^2-8bc+5c^2+b(2b+2c-a)^2