Solve 4/5left(x-7right)(x-7/2)(x-7/3

$$\frac{ 4 }{ 5 } \left( x-7 \right) ( \frac{ x-7 }{ 2 } )( \frac{ x-7 }{ 3 }$$

Evaluate

$$\frac{2\left(x-7\right)^{3}}{15}$$

Short Solution Steps

Multiply \frac{4}{5} times \frac{x-7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\left(x-7\right)}{5\times 2}\left(x-7\right)\times \frac{x-7}{3}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2\left(x-7\right)}{5}\left(x-7\right)\times \frac{x-7}{3}$$

Multiply \frac{2\left(x-7\right)}{5} times \frac{x-7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(x-7\right)\left(x-7\right)}{5\times 3}\left(x-7\right)$$

Use the distributive property to multiply \frac{2\left(x-7\right)\left(x-7\right)}{5\times 3} by x-7.

$$\frac{2\left(x-7\right)^{2}}{5\times 3}x-7\times \frac{2\left(x-7\right)\left(x-7\right)}{5\times 3}$$

Multiply x-7 and x-7 to get \left(x-7\right)^{2}.

$$\frac{2\left(x-7\right)^{2}}{5\times 3}x-7\times \frac{2\left(x-7\right)^{2}}{5\times 3}$$

Multiply 5 and 3 to get 15.

$$\frac{2\left(x-7\right)^{2}}{15}x-7\times \frac{2\left(x-7\right)^{2}}{5\times 3}$$

Express \frac{2\left(x-7\right)^{2}}{15}x as a single fraction.

$$\frac{2\left(x-7\right)^{2}x}{15}-7\times \frac{2\left(x-7\right)^{2}}{5\times 3}$$

Multiply 5 and 3 to get 15.

$$\frac{2\left(x-7\right)^{2}x}{15}-7\times \frac{2\left(x-7\right)^{2}}{15}$$

Express -7\times \frac{2\left(x-7\right)^{2}}{15} as a single fraction.

$$\frac{2\left(x-7\right)^{2}x}{15}+\frac{-7\times 2\left(x-7\right)^{2}}{15}$$

Since \frac{2\left(x-7\right)^{2}x}{15} and \frac{-7\times 2\left(x-7\right)^{2}}{15} have the same denominator, add them by adding their numerators.

$$\frac{2\left(x-7\right)^{2}x-7\times 2\left(x-7\right)^{2}}{15}$$

Do the multiplications in 2\left(x-7\right)^{2}x-7\times 2\left(x-7\right)^{2}.

$$\frac{2x^{3}-28x^{2}+98x-14x^{2}+196x-686}{15}$$

Combine like terms in 2x^{3}-28x^{2}+98x-14x^{2}+196x-686.

$$\frac{2x^{3}-42x^{2}+294x-686}{15}$$

Expand

$$\frac{2x^{3}}{15}-\frac{14x^{2}}{5}+\frac{98x}{5}-\frac{686}{15}$$

Short Solution Steps

Multiply \frac{4}{5} times \frac{x-7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\left(x-7\right)}{5\times 2}\left(x-7\right)\times \frac{x-7}{3}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2\left(x-7\right)}{5}\left(x-7\right)\times \frac{x-7}{3}$$

Multiply \frac{2\left(x-7\right)}{5} times \frac{x-7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(x-7\right)\left(x-7\right)}{5\times 3}\left(x-7\right)$$

Use the distributive property to multiply \frac{2\left(x-7\right)\left(x-7\right)}{5\times 3} by x-7.

$$\frac{2\left(x-7\right)^{2}}{5\times 3}x-7\times \frac{2\left(x-7\right)\left(x-7\right)}{5\times 3}$$

Multiply x-7 and x-7 to get \left(x-7\right)^{2}.

$$\frac{2\left(x-7\right)^{2}}{5\times 3}x-7\times \frac{2\left(x-7\right)^{2}}{5\times 3}$$

Multiply 5 and 3 to get 15.

$$\frac{2\left(x-7\right)^{2}}{15}x-7\times \frac{2\left(x-7\right)^{2}}{5\times 3}$$

Express \frac{2\left(x-7\right)^{2}}{15}x as a single fraction.

$$\frac{2\left(x-7\right)^{2}x}{15}-7\times \frac{2\left(x-7\right)^{2}}{5\times 3}$$

Multiply 5 and 3 to get 15.

$$\frac{2\left(x-7\right)^{2}x}{15}-7\times \frac{2\left(x-7\right)^{2}}{15}$$

Express -7\times \frac{2\left(x-7\right)^{2}}{15} as a single fraction.

$$\frac{2\left(x-7\right)^{2}x}{15}+\frac{-7\times 2\left(x-7\right)^{2}}{15}$$

Since \frac{2\left(x-7\right)^{2}x}{15} and \frac{-7\times 2\left(x-7\right)^{2}}{15} have the same denominator, add them by adding their numerators.

$$\frac{2\left(x-7\right)^{2}x-7\times 2\left(x-7\right)^{2}}{15}$$

Do the multiplications in 2\left(x-7\right)^{2}x-7\times 2\left(x-7\right)^{2}.

$$\frac{2x^{3}-28x^{2}+98x-14x^{2}+196x-686}{15}$$

Combine like terms in 2x^{3}-28x^{2}+98x-14x^{2}+196x-686.

$$\frac{2x^{3}-42x^{2}+294x-686}{15}$$