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Solve the following polynomial equation by grouping and factoring. 9y3−16y=0 Enter the exact answers. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1 ). The order of the list does not matter.

Solve the following polynomial equation by grouping and factoring 9y316y0 Enter the exact answers The field below accepts a list of numbers or formulas separate class=

Respuesta :

Given:

The equation

[tex]9y^3-16y=0[/tex]

Required:

Solve by factoring.

Explanation:

The steps are:

[tex]\begin{gathered} 9y^3-16y=0 \\ \text{ Take }y\text{ common}, \\ y(9y^2-16)=0 \\ \text{ Use }a^2-b^2=(a-b)(a+b) \\ y((3y)^2-4^2)=0 \\ y(3y-4)(3y+4)=0 \\ y=0,\frac{4}{3},-\frac{4}{3} \end{gathered}[/tex]

Answer:

[tex]\text{ The solution is }y=0;\frac{4}{3};-\frac{4}{3}[/tex]