Question

factorise (a-b)²+(b-c)²+(c-a)²​

Answer 1

Answer:

$= \: 2( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ac)$

Step-by-step explanation:

solution

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

$formula \: = (a - b) {}^{2} = a {}^{2} + b {}^{2} - 2ab$

$= \: \: \: (a {}^{2} + b {}^{2} - 2ab) + (b {}^{2} + c { }^{2} - 2bc) + (c {}^{2} + a {}^{2} - 2ac)$

$= \: \: a {}^{2} + {a}^{2} + {b }^{2} + {b}^{2} + {c}^{2} + {c}^{2} - 2ab - 2bc - 2ac$

$= \: \: 2 {a}^{2} + 2 {b}^{2} + 2 {c}^{2} - 2ab - 2bc - 2ac$

$= \: 2( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ac)$

Answer