Question

Find the following product:
0.1y(0.1x⁵ + 0.1y)

Answer 1

To find the product, we will use distributive law as follows:

$$\begin{gathered} 0.1y\left(0.1x^5+0.1y\right) \\ =\left(0.1y\right)\left(0.1x^5\right)+\left(0.1y\right)\left(0.1y\right) \\ =\left(0.1\times 0.1\right)\left(y\times x^5\right)+\left(0.1\times 0.1\right)\left(y\times y\right) \\ =\left(0.1\times 0.1\right)\left(x^5\times y\right)+\left(0.1\times 0.1\right)\left(y^{1+1}\right) \\ =0.01x^{5}y+0.01y^2 \end{gathered}$$

Thus, the answer is $0.01x^{5}y+0.01y^2$.