Solve (2/5x+1)(1/10x)

$$( \frac{ 2 }{ 5 } x+1)( \frac{ 1 }{ 10 } x)$$

Evaluate

$$\frac{x\left(2x+5\right)}{50}$$

Solution Steps

Use the distributive property to multiply \frac{2}{5}x+1 by \frac{1}{10}.

$$\left(\frac{2}{5}x\times \frac{1}{10}+\frac{1}{10}\right)x$$

Multiply \frac{2}{5} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\left(\frac{2\times 1}{5\times 10}x+\frac{1}{10}\right)x$$

Do the multiplications in the fraction \frac{2\times 1}{5\times 10}.

$$\left(\frac{2}{50}x+\frac{1}{10}\right)x$$

Reduce the fraction \frac{2}{50} to lowest terms by extracting and canceling out 2.

$$\left(\frac{1}{25}x+\frac{1}{10}\right)x$$

Use the distributive property to multiply \frac{1}{25}x+\frac{1}{10} by x.

$$\frac{1}{25}xx+\frac{1}{10}x$$

Multiply x and x to get x^{2}.

$$\frac{1}{25}x^{2}+\frac{1}{10}x$$

Expand

$$\frac{x^{2}}{25}+\frac{x}{10}$$

Solution Steps

Use the distributive property to multiply \frac{2}{5}x+1 by \frac{1}{10}.

$$\left(\frac{2}{5}x\times \frac{1}{10}+\frac{1}{10}\right)x$$

Multiply \frac{2}{5} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\left(\frac{2\times 1}{5\times 10}x+\frac{1}{10}\right)x$$

Do the multiplications in the fraction \frac{2\times 1}{5\times 10}.

$$\left(\frac{2}{50}x+\frac{1}{10}\right)x$$

Reduce the fraction \frac{2}{50} to lowest terms by extracting and canceling out 2.

$$\left(\frac{1}{25}x+\frac{1}{10}\right)x$$

Use the distributive property to multiply \frac{1}{25}x+\frac{1}{10} by x.

$$\frac{1}{25}xx+\frac{1}{10}x$$

Multiply x and x to get x^{2}.

$$\frac{1}{25}x^{2}+\frac{1}{10}x$$