Solve (r-1/2)(r-1/5)

$$( r - \frac { 1 } { 2 } ) ( r - \frac { 1 } { 5 } )$$

Evaluate

$$r^{2}-\frac{7r}{10}+\frac{1}{10}$$

Solution Steps

Apply the distributive property by multiplying each term of r-\frac{1}{2} by each term of r-\frac{1}{5}.

$$r^{2}+r\left(-\frac{1}{5}\right)-\frac{1}{2}r-\frac{1}{2}\left(-\frac{1}{5}\right)$$

Combine r\left(-\frac{1}{5}\right) and -\frac{1}{2}r to get -\frac{7}{10}r.

$$r^{2}-\frac{7}{10}r-\frac{1}{2}\left(-\frac{1}{5}\right)$$

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

$$r^{2}-\frac{7}{10}r+\frac{-\left(-1\right)}{2\times 5}$$

Do the multiplications in the fraction \frac{-\left(-1\right)}{2\times 5}.

$$r^{2}-\frac{7}{10}r+\frac{1}{10}$$

Expand

$$r^{2}-\frac{7r}{10}+\frac{1}{10}$$

Solution Steps

Apply the distributive property by multiplying each term of r-\frac{1}{2} by each term of r-\frac{1}{5}.

$$r^{2}+r\left(-\frac{1}{5}\right)-\frac{1}{2}r-\frac{1}{2}\left(-\frac{1}{5}\right)$$

Combine r\left(-\frac{1}{5}\right) and -\frac{1}{2}r to get -\frac{7}{10}r.

$$r^{2}-\frac{7}{10}r-\frac{1}{2}\left(-\frac{1}{5}\right)$$

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

$$r^{2}-\frac{7}{10}r+\frac{-\left(-1\right)}{2\times 5}$$

Do the multiplications in the fraction \frac{-\left(-1\right)}{2\times 5}.

$$r^{2}-\frac{7}{10}r+\frac{1}{10}$$