Question

Multiply the first expression by the second (a2 + b2 + c2 –ab – bc – ca), (a + b + c)

Answer 1

SOLUTION

TO MULTIPLY

$\sf{ ({a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca) \: \: and \: \: (a + b + c) }$

EVALUATION

The required result

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

$\sf{ = {a}^{3} + {a}^{2}b + {a}^{2} c + a {b}^{2} + {b}^{3} + {b}^{2} c }$

$\sf{ + a {c}^{2} + b {c}^{2} + {c}^{3} - {a}^{2} b - a {b}^{2} - abc }$

$\sf{ - abc - {b}^{2}c - b {c}^{2} - {a}^{2} c - abc - a {c}^{2} }$

$= \sf{ {a}^{3} + {b}^{3} + {c}^{3} - 3abc }$

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