What is 1/(2(a+b+c)[(a-b)^2+(b-c)^2+(c-a)^2]) ?

The solution to 1/(2(a+b+c)[(a-b)^2+(b-c)^2+(c-a)^2]) is 1/(2(a+b+c)(2a^2-2ab+2b^2-2bc+2c^2-2ac))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 1/(2(a+b+c)[(a-b)^2+(b-c)^2+(c-a)^2])

simplify

\frac{1}{2 ( a + b + c ) [ ( a - b ) ^{2} + ( b - c ) ^{2} + ( c - a ) ^{2} ]}

\frac{1}{2 ( a + b + c ) ( 2 a ^{2} - 2 ab + 2 b ^{2} - 2 b c + 2 c ^{2} - 2 a c )}

Solution steps

\frac{1}{2 ( a + b + c ) ( ( a - b ) ^{2} + ( b - c ) ^{2} + ( c - a ) ^{2} )}

Expand

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

= \frac{1}{2 ( a + b + c ) ( a ^{2} - 2 ab + b ^{2} + ( b - c ) ^{2} + ( c - a ) ^{2} )}

Expand

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

= \frac{1}{2 ( a + b + c ) ( a ^{2} - 2 ab + b ^{2} + b ^{2} - 2 b c + c ^{2} + ( c - a ) ^{2} )}

Expand

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

= \frac{1}{2 ( a + b + c ) ( a ^{2} - 2 ab + b ^{2} + b ^{2} - 2 b c + c ^{2} + c ^{2} - 2 a c + a ^{2} )}

Simplify

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

= \frac{1}{2 ( a + b + c ) ( 2 a ^{2} - 2 ab + 2 b ^{2} - 2 b c + 2 c ^{2} - 2 a c )}

3^{x - 2} - 3^{2}

3 x + (- 3 y) - (4 x)

\frac{1}{x} + 1 + 2 \frac{x}{x ^{2}} - 1 - \frac{1}{x} - 1

2 - 16 x^{3}

(- 5 a^{4})^{2}

What is 1/(2(a+b+c)[(a-b)^2+(b-c)^2+(c-a)^2]) ?
The solution to 1/(2(a+b+c)[(a-b)^2+(b-c)^2+(c-a)^2]) is 1/(2(a+b+c)(2a^2-2ab+2b^2-2bc+2c^2-2ac))