Question

Factorise (a-b)^3+ (b-c)^3+(c-a)^3

Answer 1

$\huge\boxed{\underline{\mathcal{\red{A}\green{N}\pink{S}\orange{W}\blue{E}\pink{R}}}}$

Answer 2

${ \huge \bf{ \mid{ \overline{ \underline{ \red{QUESTION}}}} \mid}} \longrightarrow$

$\mathtt{ \green{factorize = (a - b {)}^{ 3} + (b - c) {}^{3} + (c - a) {}^{3} }}$

${ \huge{ \mathbb{ \underbrace{ \purple { \boxed{ \red{ \underline{ \underline{ \green{ANSWER}}}}}}}}}}$

$\huge{ \orange{ formula \: used}} = >$

$\boxed{ \fbox{ \purple{(a - b) {}^{3} = {a}^{3} - {b}^{3} - 3ab(a - b) }}}$

$\tiny{a }^{3} - {b}^{3} - 3ab(a - b) + {b}^{3} - c {}^{3} - 3bc(b - c) + {c}^{3} - {a}^{3} - 3ca(c - a) \\ \tiny = > - 3ab(a - b) - 3bc(b - c) - 3ca(c - a) \\ = > - 3{[ab(a - b) + bc(b - c) + ca(c - a)]}$