Solve x^2/25-y^2/16

$$\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 }$$

Factor

$$\frac{\left(4x-5y\right)\left(4x+5y\right)}{400}$$

Solution Steps

Factor out \frac{1}{400}.

$$\frac{16x^{2}-25y^{2}}{400}$$

Consider 16x^{2}-25y^{2}. Rewrite 16x^{2}-25y^{2} as \left(4x\right)^{2}-\left(5y\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(4x-5y\right)\left(4x+5y\right)$$

Rewrite the complete factored expression.

$$\frac{\left(4x-5y\right)\left(4x+5y\right)}{400}$$

Evaluate

$$\frac{x^{2}}{25}-\frac{y^{2}}{16}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25 and 16 is 400. Multiply \frac{x^{2}}{25} times \frac{16}{16}. Multiply \frac{y^{2}}{16} times \frac{25}{25}.

$$\frac{16x^{2}}{400}-\frac{25y^{2}}{400}$$

Since \frac{16x^{2}}{400} and \frac{25y^{2}}{400} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16x^{2}-25y^{2}}{400}$$