Solve:
[tex]9y^3-16y=0[/tex]Factoring out y:
[tex]y(9y^2-16)=0[/tex]The expression in parentheses can be factored by using the special product:
[tex]a^2-b^2=(a-b)(a+b)[/tex]Therefore, the equation becomes:
[tex]y(3y-4)(3y+4)=0[/tex]Now equate each factor to 0 and solve for y:
[tex]\begin{gathered} y=0 \\ \\ 3y-4=0\therefore y=\frac{4}{3} \\ \\ 3y+4=0\therefore y=-\frac{4}{3} \end{gathered}[/tex]We have 3 solutions:
y = 0, y = 4/3, y = -4/3
