Question 24979
Factor:
{{{6y^4 - 486}}} First, factor a 6.
{{{6(y^4 - 81)}}} The parentheses contain the difference of two squares.
{{{6((y^2)^2 - 9^2)}}} This can be factored.
{{{6(y^2 - 9)(y^2 + 9)}}} Now the {{{(y^2 - 9)}}} is the difference of two squares and can be factored.
{{{6(y - 3)(y + 3)(y^2 + 9)}}}
Normally we would stop here, but if you are into complex binomials, you can go one step farther. {{{(a^2 + b^2)}}} will factor as {{{(a - bi)(a + bi)}}}, so:
{{{6(y - 3)(y + 3)(y - 3i)(y + 3i)}}} would be the complete factorisation.