Solve 1/2(6x/8)x(8-x)

$$\frac { 1 } { 2 } ( \frac { 6 x } { 8 } ) x ( 8 - x )$$

Evaluate

$$-\frac{3x^{3}}{8}+3x^{2}$$

Solution Steps

Divide 6x by 8 to get \frac{3}{4}x.

$$\frac{1}{2}\times \frac{3}{4}xx\left(8-x\right)$$

Multiply \frac{1}{2} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3}{2\times 4}xx\left(8-x\right)$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 4}.

$$\frac{3}{8}xx\left(8-x\right)$$

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

$$\frac{3}{8}x^{2}\left(8-x\right)$$

Use the distributive property to multiply \frac{3}{8}x^{2} by 8-x.

$$\frac{3}{8}x^{2}\times 8+\frac{3}{8}x^{2}\left(-1\right)x$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{3}{8}x^{2}\times 8+\frac{3}{8}x^{3}\left(-1\right)$$

Cancel out 8 and 8.

$$3x^{2}+\frac{3}{8}x^{3}\left(-1\right)$$

Multiply \frac{3}{8} and -1 to get -\frac{3}{8}.

$$3x^{2}-\frac{3}{8}x^{3}$$

Expand

$$-\frac{3x^{3}}{8}+3x^{2}$$

Solution Steps

Divide 6x by 8 to get \frac{3}{4}x.

$$\frac{1}{2}\times \frac{3}{4}xx\left(8-x\right)$$

Multiply \frac{1}{2} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3}{2\times 4}xx\left(8-x\right)$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 4}.

$$\frac{3}{8}xx\left(8-x\right)$$

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

$$\frac{3}{8}x^{2}\left(8-x\right)$$

Use the distributive property to multiply \frac{3}{8}x^{2} by 8-x.

$$\frac{3}{8}x^{2}\times 8+\frac{3}{8}x^{2}\left(-1\right)x$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{3}{8}x^{2}\times 8+\frac{3}{8}x^{3}\left(-1\right)$$

Cancel out 8 and 8.

$$3x^{2}+\frac{3}{8}x^{3}\left(-1\right)$$

Multiply \frac{3}{8} and -1 to get -\frac{3}{8}.

$$3x^{2}-\frac{3}{8}x^{3}$$