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

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

Evaluate

$$4n^{2}-\frac{3n}{2}+\frac{1}{8}$$

Solution Steps

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

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

Express 2\left(-\frac{1}{4}\right) as a single fraction.

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

Multiply 2 and -1 to get -2.

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

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

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

Cancel out 2 and 2.

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

Combine -\frac{1}{2}n and -n to get -\frac{3}{2}n.

$$4n^{2}-\frac{3}{2}n-\frac{1}{2}\left(-\frac{1}{4}\right)$$

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

$$4n^{2}-\frac{3}{2}n+\frac{-\left(-1\right)}{2\times 4}$$

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

$$4n^{2}-\frac{3}{2}n+\frac{1}{8}$$

Expand

$$4n^{2}-\frac{3n}{2}+\frac{1}{8}$$

Solution Steps

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

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

Express 2\left(-\frac{1}{4}\right) as a single fraction.

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

Multiply 2 and -1 to get -2.

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

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

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

Cancel out 2 and 2.

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

Combine -\frac{1}{2}n and -n to get -\frac{3}{2}n.

$$4n^{2}-\frac{3}{2}n-\frac{1}{2}\left(-\frac{1}{4}\right)$$

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

$$4n^{2}-\frac{3}{2}n+\frac{-\left(-1\right)}{2\times 4}$$

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

$$4n^{2}-\frac{3}{2}n+\frac{1}{8}$$