Solve (2n-1/2)(2n-1/9)

$$( 2 n - \frac { 1 } { 2 } ) ( 2 n - \frac { 1 } { 9 } )$$

Evaluate

$$4n^{2}-\frac{11n}{9}+\frac{1}{18}$$

Solution Steps

Apply the distributive property by multiplying each term of 2n-\frac{1}{2} by each term of 2n-\frac{1}{9}.

$$4n^{2}+2n\left(-\frac{1}{9}\right)-\frac{1}{2}\times 2n-\frac{1}{2}\left(-\frac{1}{9}\right)$$

Express 2\left(-\frac{1}{9}\right) as a single fraction.

$$4n^{2}+\frac{2\left(-1\right)}{9}n-\frac{1}{2}\times 2n-\frac{1}{2}\left(-\frac{1}{9}\right)$$

Multiply 2 and -1 to get -2.

$$4n^{2}+\frac{-2}{9}n-\frac{1}{2}\times 2n-\frac{1}{2}\left(-\frac{1}{9}\right)$$

Fraction \frac{-2}{9} can be rewritten as -\frac{2}{9} by extracting the negative sign.

$$4n^{2}-\frac{2}{9}n-\frac{1}{2}\times 2n-\frac{1}{2}\left(-\frac{1}{9}\right)$$

Cancel out 2 and 2.

$$4n^{2}-\frac{2}{9}n-n-\frac{1}{2}\left(-\frac{1}{9}\right)$$

Combine -\frac{2}{9}n and -n to get -\frac{11}{9}n.

$$4n^{2}-\frac{11}{9}n-\frac{1}{2}\left(-\frac{1}{9}\right)$$

Multiply -\frac{1}{2} times -\frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$4n^{2}-\frac{11}{9}n+\frac{-\left(-1\right)}{2\times 9}$$

Do the multiplications in the fraction \frac{-\left(-1\right)}{2\times 9}.

$$4n^{2}-\frac{11}{9}n+\frac{1}{18}$$

Expand

$$4n^{2}-\frac{11n}{9}+\frac{1}{18}$$

Solution Steps

Apply the distributive property by multiplying each term of 2n-\frac{1}{2} by each term of 2n-\frac{1}{9}.

$$4n^{2}+2n\left(-\frac{1}{9}\right)-\frac{1}{2}\times 2n-\frac{1}{2}\left(-\frac{1}{9}\right)$$

Express 2\left(-\frac{1}{9}\right) as a single fraction.

$$4n^{2}+\frac{2\left(-1\right)}{9}n-\frac{1}{2}\times 2n-\frac{1}{2}\left(-\frac{1}{9}\right)$$

Multiply 2 and -1 to get -2.

$$4n^{2}+\frac{-2}{9}n-\frac{1}{2}\times 2n-\frac{1}{2}\left(-\frac{1}{9}\right)$$

Fraction \frac{-2}{9} can be rewritten as -\frac{2}{9} by extracting the negative sign.

$$4n^{2}-\frac{2}{9}n-\frac{1}{2}\times 2n-\frac{1}{2}\left(-\frac{1}{9}\right)$$

Cancel out 2 and 2.

$$4n^{2}-\frac{2}{9}n-n-\frac{1}{2}\left(-\frac{1}{9}\right)$$

Combine -\frac{2}{9}n and -n to get -\frac{11}{9}n.

$$4n^{2}-\frac{11}{9}n-\frac{1}{2}\left(-\frac{1}{9}\right)$$

Multiply -\frac{1}{2} times -\frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$4n^{2}-\frac{11}{9}n+\frac{-\left(-1\right)}{2\times 9}$$

Do the multiplications in the fraction \frac{-\left(-1\right)}{2\times 9}.

$$4n^{2}-\frac{11}{9}n+\frac{1}{18}$$