Solve y^5-16y^3b^2

$$y ^ { 5 } - 16 y ^ { 3 } b ^ { 2 }$$

Factor

$$\left(y-4b\right)\left(y+4b\right)y^{3}$$

Solution Steps

Factor out y^{3}.

$$y^{3}\left(y^{2}-16b^{2}\right)$$

Consider y^{2}-16b^{2}. Rewrite y^{2}-16b^{2} as y^{2}-\left(4b\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(y-4b\right)\left(y+4b\right)$$

Rewrite the complete factored expression.

$$y^{3}\left(y-4b\right)\left(y+4b\right)$$

Evaluate

$$\left(y^{2}-16b^{2}\right)y^{3}$$