Solve 1(x-7)(x-7/2)

$$1(x-7)( \frac{ x-7 }{ 2 } )$$

Evaluate

$$\frac{\left(x-7\right)^{2}}{2}$$

Short Solution Steps

Express 1\times \frac{x-7}{2} as a single fraction.

$$\frac{x-7}{2}\left(x-7\right)$$

Use the distributive property to multiply \frac{x-7}{2} by x-7.

$$\frac{x-7}{2}x-7\times \frac{x-7}{2}$$

Express \frac{x-7}{2}x as a single fraction.

$$\frac{\left(x-7\right)x}{2}-7\times \frac{x-7}{2}$$

Express -7\times \frac{x-7}{2} as a single fraction.

$$\frac{\left(x-7\right)x}{2}+\frac{-7\left(x-7\right)}{2}$$

Since \frac{\left(x-7\right)x}{2} and \frac{-7\left(x-7\right)}{2} have the same denominator, add them by adding their numerators.

$$\frac{\left(x-7\right)x-7\left(x-7\right)}{2}$$

Do the multiplications in \left(x-7\right)x-7\left(x-7\right).

$$\frac{x^{2}-7x-7x+49}{2}$$

Combine like terms in x^{2}-7x-7x+49.

$$\frac{x^{2}-14x+49}{2}$$

Expand

$$\frac{x^{2}}{2}-7x+\frac{49}{2}$$

Short Solution Steps

Express 1\times \frac{x-7}{2} as a single fraction.

$$\frac{x-7}{2}\left(x-7\right)$$

Use the distributive property to multiply \frac{x-7}{2} by x-7.

$$\frac{x-7}{2}x-7\times \frac{x-7}{2}$$

Express \frac{x-7}{2}x as a single fraction.

$$\frac{\left(x-7\right)x}{2}-7\times \frac{x-7}{2}$$

Express -7\times \frac{x-7}{2} as a single fraction.

$$\frac{\left(x-7\right)x}{2}+\frac{-7\left(x-7\right)}{2}$$

Since \frac{\left(x-7\right)x}{2} and \frac{-7\left(x-7\right)}{2} have the same denominator, add them by adding their numerators.

$$\frac{\left(x-7\right)x-7\left(x-7\right)}{2}$$

Do the multiplications in \left(x-7\right)x-7\left(x-7\right).

$$\frac{x^{2}-7x-7x+49}{2}$$

Combine like terms in x^{2}-7x-7x+49.

$$\frac{x^{2}-14x+49}{2}$$