Question

(a-b-c)^3 what is the formula​

Answer 1

Answer:

a³ - b³ - c³ - 3(b + c)(a - b)(a - c)  

Step-by-step explanation:

(a - b - c)³ = [a - (b + c)]³

let (b+c) be X

//remember  (a - b)³ = a³ - 3a²b + 3ab² - b³

[a - X]³ = a³ - 3a²X + 3aX² - X³

 //substitute value of X back in the above

   =  a³ - 3a²(b + c) + 3a(b + c)² - (b + c)³

   = a³ - 3a²(b + c) + 3a(b + c)² - (b³ + 3b²c + 3bc² + c³)

   //re-arrange the equation

 = a³ - b³ - c³ - 3{a²(b + c) - a(b + c)² + (b²c + bc²)}

 = a³ - b³ - c³ - 3{a²(b + c) - a(b + c)² + bc(b + c)}

= a³ - b³ - c³ - 3(b + c){a² - ab - ac + bc}

= a³ - b³ - c³ - 3(b + c){a(a - b) - c(a - b)}

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