Question

One of the factors of a³ – 3a²b + 3ab² – b³ is 

A) – 3ab 

B) 3ab 

C) a + b 

D) a – b

Answer 1

Correct option is (D) a – b

\(a^ 3-3a^2b+3ab^2-b^3\) \(=a^3-a^2b-2a^2b+2ab^2+ab^2-b^3\)

\(=a^2(a-b)-2ab(a-b)+b^2(a-b)\)

\(=(a-b)(a^2-2ab+b^2)\)

\(=(a-b)(a-b)^2\)

\(=(a-b)^3\)

\(\therefore\) Factor of \(a^ 3-3a^2b+3ab^2-b^3\) is (a – b).

Answer 2

Correct option is  D) a – b