Factorization of a³ + b³ + 3ab − 1
The factorized form of \[ a^3+b^3+3ab-1 \] is _________
Solution
\[ a^3+b^3+3ab-1 \]
\[ =a^3+b^3+(-1)^3-3ab(-1) \]
Using identity:
\[ x^3+y^3+z^3-3xyz =(x+y+z)(x^2+y^2+z^2-xy-yz-zx) \]
\[ = (a+b-1) \left(a^2+b^2+1-ab+b+a\right) \]
\[ \boxed{(a+b-1)(a^2+b^2+1-ab+a+b)} \]