Solve left(4-4x^2/z^2right)(2/z)

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{z^{2}}{z^{2}}.

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

Since \frac{4z^{2}}{z^{2}} and \frac{4x^{2}}{z^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4z^{2}-4x^{2}}{z^{2}}\times \frac{2}{z}$$

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

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

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

$$\frac{\left(4z^{2}-4x^{2}\right)\times 2}{z^{3}}$$

Use the distributive property to multiply 4z^{2}-4x^{2} by 2.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{z^{2}}{z^{2}}.

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

Since \frac{4z^{2}}{z^{2}} and \frac{4x^{2}}{z^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4z^{2}-4x^{2}}{z^{2}}\times \frac{2}{z}$$

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

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

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

$$\frac{\left(4z^{2}-4x^{2}\right)\times 2}{z^{3}}$$

Use the distributive property to multiply 4z^{2}-4x^{2} by 2.

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