Question

Divide the polynomial by the binomial.

$\left(125y^3-64\right)÷\left(5y-4\right)$

Short answer

The solution is$25y^2+20y+16$.

Step-by-step solution

Step 1. Given information.

The given expression is$\left(125y^3-64\right)÷\left(5y-4\right)$.

Step 2. Divide the polynomial by a binomial by using the long division method.

Solve it as follows:

$$\begin{gathered} 5y-4\begin{array}{ccc}25y^2& +20y& +16\end{array}\begin{array}{cccc}125y^3& +0y^2& +0y& -64\\ 125y^3& -100y^2& & \end{array} \\ \overline{100y^2+0y} \\ 100y^2-80y \\ \overline{80y-64} \\ 80y-64 \\ \overline{0} \end{gathered}$$

Step 3. Simplified expression.

Hence, the obtained result is $25y^2+20y+16$.