Solve d^2/100-e^2/9

$$\frac { d ^ { 2 } } { 100 } - \frac { e ^ { 2 } } { 9 }$$

Factor

$$\frac{\left(3d-10e\right)\left(3d+10e\right)}{900}$$

Solution Steps

Factor out \frac{1}{900}.

$$\frac{9d^{2}-100e^{2}}{900}$$

Consider 9d^{2}-100e^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3d-10e\right)\left(3d+10e\right)$$

Rewrite the complete factored expression.

$$\frac{\left(3d-10e\right)\left(3d+10e\right)}{900}$$

Evaluate

$$\frac{d^{2}}{100}-\frac{e^{2}}{9}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 100 and 9 is 900. Multiply \frac{d^{2}}{100} times \frac{9}{9}. Multiply \frac{e^{2}}{9} times \frac{100}{100}.

$$\frac{9d^{2}}{900}-\frac{100e^{2}}{900}$$

Since \frac{9d^{2}}{900} and \frac{100e^{2}}{900} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9d^{2}-100e^{2}}{900}$$