Solve =22000/(1+r)^2-18000

$$= \frac { 22000 } { ( 1 + r ) ^ { 2 } } - 18000$$

Evaluate

$$\frac{2000\left(2-18r-9r^{2}\right)}{\left(r+1\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 18000 times \frac{\left(1+r\right)^{2}}{\left(1+r\right)^{2}}.

$$\frac{22000}{\left(1+r\right)^{2}}-\frac{18000\left(1+r\right)^{2}}{\left(1+r\right)^{2}}$$

Since \frac{22000}{\left(1+r\right)^{2}} and \frac{18000\left(1+r\right)^{2}}{\left(1+r\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22000-18000\left(1+r\right)^{2}}{\left(1+r\right)^{2}}$$

Do the multiplications in 22000-18000\left(1+r\right)^{2}.

$$\frac{22000-18000-36000r-18000r^{2}}{\left(1+r\right)^{2}}$$

Combine like terms in 22000-18000-36000r-18000r^{2}.

$$\frac{4000-36000r-18000r^{2}}{\left(1+r\right)^{2}}$$

Expand \left(1+r\right)^{2}.

$$\frac{4000-36000r-18000r^{2}}{r^{2}+2r+1}$$

Expand

$$-\frac{2000\left(9r^{2}+18r-2\right)}{\left(r+1\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 18000 times \frac{\left(1+r\right)^{2}}{\left(1+r\right)^{2}}.

$$\frac{22000}{\left(1+r\right)^{2}}-\frac{18000\left(1+r\right)^{2}}{\left(1+r\right)^{2}}$$

Since \frac{22000}{\left(1+r\right)^{2}} and \frac{18000\left(1+r\right)^{2}}{\left(1+r\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22000-18000\left(1+r\right)^{2}}{\left(1+r\right)^{2}}$$

Do the multiplications in 22000-18000\left(1+r\right)^{2}.

$$\frac{22000-18000-36000r-18000r^{2}}{\left(1+r\right)^{2}}$$

Combine like terms in 22000-18000-36000r-18000r^{2}.

$$\frac{4000-36000r-18000r^{2}}{\left(1+r\right)^{2}}$$

Expand \left(1+r\right)^{2}.

$$\frac{4000-36000r-18000r^{2}}{r^{2}+2r+1}$$