Solve (5n+1/2)(4n-4/5)

$$( 5 n + \frac { 1 } { 2 } ) ( 4 n - \frac { 4 } { 5 } )$$

Evaluate

$$20n^{2}-2n-\frac{2}{5}$$

Solution Steps

Apply the distributive property by multiplying each term of 5n+\frac{1}{2} by each term of 4n-\frac{4}{5}.

$$20n^{2}+5n\left(-\frac{4}{5}\right)+\frac{1}{2}\times 4n+\frac{1}{2}\left(-\frac{4}{5}\right)$$

Cancel out 5 and 5.

$$20n^{2}-4n+\frac{1}{2}\times 4n+\frac{1}{2}\left(-\frac{4}{5}\right)$$

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$20n^{2}-4n+\frac{4}{2}n+\frac{1}{2}\left(-\frac{4}{5}\right)$$

Divide 4 by 2 to get 2.

$$20n^{2}-4n+2n+\frac{1}{2}\left(-\frac{4}{5}\right)$$

Combine -4n and 2n to get -2n.

$$20n^{2}-2n+\frac{1}{2}\left(-\frac{4}{5}\right)$$

Multiply \frac{1}{2} times -\frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$20n^{2}-2n+\frac{1\left(-4\right)}{2\times 5}$$

Do the multiplications in the fraction \frac{1\left(-4\right)}{2\times 5}.

$$20n^{2}-2n+\frac{-4}{10}$$

Reduce the fraction \frac{-4}{10} to lowest terms by extracting and canceling out 2.

$$20n^{2}-2n-\frac{2}{5}$$

Expand

$$20n^{2}-2n-\frac{2}{5}$$

Solution Steps

Apply the distributive property by multiplying each term of 5n+\frac{1}{2} by each term of 4n-\frac{4}{5}.

$$20n^{2}+5n\left(-\frac{4}{5}\right)+\frac{1}{2}\times 4n+\frac{1}{2}\left(-\frac{4}{5}\right)$$

Cancel out 5 and 5.

$$20n^{2}-4n+\frac{1}{2}\times 4n+\frac{1}{2}\left(-\frac{4}{5}\right)$$

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$20n^{2}-4n+\frac{4}{2}n+\frac{1}{2}\left(-\frac{4}{5}\right)$$

Divide 4 by 2 to get 2.

$$20n^{2}-4n+2n+\frac{1}{2}\left(-\frac{4}{5}\right)$$

Combine -4n and 2n to get -2n.

$$20n^{2}-2n+\frac{1}{2}\left(-\frac{4}{5}\right)$$

Multiply \frac{1}{2} times -\frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$20n^{2}-2n+\frac{1\left(-4\right)}{2\times 5}$$

Do the multiplications in the fraction \frac{1\left(-4\right)}{2\times 5}.

$$20n^{2}-2n+\frac{-4}{10}$$

Reduce the fraction \frac{-4}{10} to lowest terms by extracting and canceling out 2.

$$20n^{2}-2n-\frac{2}{5}$$