What is 15(a-b+c)^2+(b-c+a)^2+2(a-b+c)(b-c+a) ?

The solution to 15(a-b+c)^2+(b-c+a)^2+2(a-b+c)(b-c+a) is 15(a-b+c)^2-b^2+3a^2+2bc+2ab-c^2-2ac

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simplify 15(a-b+c)^2+(b-c+a)^2+2(a-b+c)(b-c+a)

simplify

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

15 (a - b + c)^{2} - b^{2} + 3 a^{2} + 2 b c + 2 ab - c^{2} - 2 a c

Solution steps

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

Expand

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

= 15 (a - b + c)^{2} + b^{2} - 2 b c + 2 ab + c^{2} + a^{2} - 2 a c + 2 (a - b + c) (b - c + a)

Expand

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

= 15 (a - b + c)^{2} + b^{2} - 2 b c + 2 ab + c^{2} + a^{2} - 2 a c + 2 a^{2} - 2 b^{2} + 4 b c - 2 c^{2}

Group like terms

= 15 (a - b + c)^{2} + b^{2} - 2 b^{2} + 2 a^{2} + a^{2} - 2 b c + 4 b c + 2 ab + c^{2} - 2 c^{2} - 2 a c

Add similar elements:

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

= 15 (a - b + c)^{2} - b^{2} + 2 a^{2} + a^{2} - 2 b c + 4 b c + 2 ab + c^{2} - 2 c^{2} - 2 a c

Add similar elements:

2 a^{2} + a^{2} = 3 a^{2}

= 15 (a - b + c)^{2} - b^{2} + 3 a^{2} - 2 b c + 4 b c + 2 ab + c^{2} - 2 c^{2} - 2 a c

Add similar elements:

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

= 15 (a - b + c)^{2} - b^{2} + 3 a^{2} + 2 b c + 2 ab + c^{2} - 2 c^{2} - 2 a c

Add similar elements:

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

= 15 (a - b + c)^{2} - b^{2} + 3 a^{2} + 2 b c + 2 ab - c^{2} - 2 a c

\frac{( x ) 1}{( lo g _{x} ( 7 ) )}

(z^{2})^{- 1} 0

3 (2 x - 3) 2 (x + 5) - 1

(\frac{a}{2} + \frac{2}{a})^{2}

64 x^{2} y^{2} - 121 z^{2}

What is 15(a-b+c)^2+(b-c+a)^2+2(a-b+c)(b-c+a) ?
The solution to 15(a-b+c)^2+(b-c+a)^2+2(a-b+c)(b-c+a) is 15(a-b+c)^2-b^2+3a^2+2bc+2ab-c^2-2ac