Solve (5n-4/5)(5n-1/5)

$$( 5 n - \frac { 4 } { 5 } ) ( 5 n - \frac { 1 } { 5 } )$$

Evaluate

$$25n^{2}-5n+\frac{4}{25}$$

Solution Steps

Apply the distributive property by multiplying each term of 5n-\frac{4}{5} by each term of 5n-\frac{1}{5}.

$$25n^{2}+5n\left(-\frac{1}{5}\right)-\frac{4}{5}\times 5n-\frac{4}{5}\left(-\frac{1}{5}\right)$$

Cancel out 5 and 5.

$$25n^{2}-n-\frac{4}{5}\times 5n-\frac{4}{5}\left(-\frac{1}{5}\right)$$

Cancel out 5 and 5.

$$25n^{2}-n-4n-\frac{4}{5}\left(-\frac{1}{5}\right)$$

Combine -n and -4n to get -5n.

$$25n^{2}-5n-\frac{4}{5}\left(-\frac{1}{5}\right)$$

Multiply -\frac{4}{5} times -\frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$25n^{2}-5n+\frac{-4\left(-1\right)}{5\times 5}$$

Do the multiplications in the fraction \frac{-4\left(-1\right)}{5\times 5}.

$$25n^{2}-5n+\frac{4}{25}$$

Expand

$$25n^{2}-5n+\frac{4}{25}$$

Solution Steps

Apply the distributive property by multiplying each term of 5n-\frac{4}{5} by each term of 5n-\frac{1}{5}.

$$25n^{2}+5n\left(-\frac{1}{5}\right)-\frac{4}{5}\times 5n-\frac{4}{5}\left(-\frac{1}{5}\right)$$

Cancel out 5 and 5.

$$25n^{2}-n-\frac{4}{5}\times 5n-\frac{4}{5}\left(-\frac{1}{5}\right)$$

Cancel out 5 and 5.

$$25n^{2}-n-4n-\frac{4}{5}\left(-\frac{1}{5}\right)$$

Combine -n and -4n to get -5n.

$$25n^{2}-5n-\frac{4}{5}\left(-\frac{1}{5}\right)$$

Multiply -\frac{4}{5} times -\frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$25n^{2}-5n+\frac{-4\left(-1\right)}{5\times 5}$$

Do the multiplications in the fraction \frac{-4\left(-1\right)}{5\times 5}.

$$25n^{2}-5n+\frac{4}{25}$$