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

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

Evaluate

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

Solution Steps

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

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

Multiply x and x to get x^{2}.

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

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

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

Cancel out 2 in both numerator and denominator.

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

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

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

Cancel out 2 in both numerator and denominator.

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

Fraction \frac{-1}{5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

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

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

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

Do the multiplications in the fraction \frac{4\times 1}{5\times 2}.

$$\frac{1}{5}x^{2}-\frac{1}{5}x+\frac{4}{10}x+\frac{4}{5}\left(-\frac{1}{2}\right)$$

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

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

Combine -\frac{1}{5}x and \frac{2}{5}x to get \frac{1}{5}x.

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

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

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

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

$$\frac{1}{5}x^{2}+\frac{1}{5}x+\frac{-4}{10}$$

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

$$\frac{1}{5}x^{2}+\frac{1}{5}x-\frac{2}{5}$$

Expand

$$\frac{x^{2}+x-2}{5}$$

Solution Steps

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

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

Multiply x and x to get x^{2}.

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

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

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

Cancel out 2 in both numerator and denominator.

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

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

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

Cancel out 2 in both numerator and denominator.

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

Fraction \frac{-1}{5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

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

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

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

Do the multiplications in the fraction \frac{4\times 1}{5\times 2}.

$$\frac{1}{5}x^{2}-\frac{1}{5}x+\frac{4}{10}x+\frac{4}{5}\left(-\frac{1}{2}\right)$$

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

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

Combine -\frac{1}{5}x and \frac{2}{5}x to get \frac{1}{5}x.

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

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

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

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

$$\frac{1}{5}x^{2}+\frac{1}{5}x+\frac{-4}{10}$$

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

$$\frac{1}{5}x^{2}+\frac{1}{5}x-\frac{2}{5}$$