Solve 1/2(1-1/2x)x

$$\frac{ 1 }{ 2 } (1- \frac{ 1 }{ 2 } x)x$$

Evaluate

$$\frac{x\left(2-x\right)}{4}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 1-\frac{1}{2}x.

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

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

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

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

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

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

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

Use the distributive property to multiply \frac{1}{2}-\frac{1}{4}x by x.

$$\frac{1}{2}x-\frac{1}{4}xx$$

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

$$\frac{1}{2}x-\frac{1}{4}x^{2}$$

Expand

$$-\frac{x^{2}}{4}+\frac{x}{2}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 1-\frac{1}{2}x.

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

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

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

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

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

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

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

Use the distributive property to multiply \frac{1}{2}-\frac{1}{4}x by x.

$$\frac{1}{2}x-\frac{1}{4}xx$$

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

$$\frac{1}{2}x-\frac{1}{4}x^{2}$$