Factorize:
@^ (y^3 - y) @^
Answer:
^@ y ( y - 1 ) ( y + 1 )^@
- We know that @^ \begin{aligned} (a^2 - b^2) = (a + b) (a - b) \end{aligned} @^
- Thus @^ \begin{aligned} (y^3 - y) = \space& y( y^2 - 1 ) \\ = \space& y( y^2 - 1^2 ) \\ = \space& y ( y - 1 ) ( y + 1 ) \end{aligned} @^
- Thus, ^@ (y^3 - y) = y ( y - 1 ) ( y + 1 )^@.
