Question

A factor of [a+b+c]3 - a3-b3-c3? with solution..

Answer 1

Answer:

we know that,

[a+b+c]³ = a³+b³+c³+3(a+b)(b+c)(c+a)

=> [a+b+c]³- a³-b³-c³ = 3(a+b)(b+c)(c+a)

Answer 2

Given:

[a + b + c]³ - a³ - b³ - c³

To find:

The factors of the given expression.

Solution:

[a + b + c]³ - a³ - b³ - c³.

= [a + b + c]²[a + b + c] - a³ - b³ - c³.

= [a² + b² + c² + 2(ab + bc + ca)][a + b + c] - a³ - b³ - c³.

= [a² + b² + c² + 2ab + 2bc + 2ca][a + b + c] - a³ - b³ - c³.

= a³ + a²b + a²c + ab² + b³ + b²c + ac² + bc² + c³ + 2a²b + 2ab² + 2abc + 2abc + 2b²c + 2bc² + 2a²c + 2abc + 2ac² - a³ - b³ - c³.

= 3a²b + 3a²c + 3ab² + 3b²c + 3ac² + 3bc² + 6abc.

= 3(a + b)(b + c)(c + a).

Hence the factors of the given expression are 3(a + b)(b + c)(c + a).