Solve 9x^2-y^2/100

$$9 x ^ { 2 } - \frac { y ^ { 2 } } { 100 }$$

Evaluate

$$-\frac{y^{2}}{100}+9x^{2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 9x^{2} times \frac{100}{100}.

$$\frac{100\times 9x^{2}}{100}-\frac{y^{2}}{100}$$

Since \frac{100\times 9x^{2}}{100} and \frac{y^{2}}{100} have the same denominator, subtract them by subtracting their numerators.

$$\frac{100\times 9x^{2}-y^{2}}{100}$$

Do the multiplications in 100\times 9x^{2}-y^{2}.

$$\frac{900x^{2}-y^{2}}{100}$$

Factor

$$\frac{\left(30x-y\right)\left(30x+y\right)}{100}$$

Solution Steps

Factor out \frac{1}{100}.

$$\frac{900x^{2}-y^{2}}{100}$$

Consider 900x^{2}-y^{2}. Rewrite 900x^{2}-y^{2} as \left(30x\right)^{2}-y^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(30x-y\right)\left(30x+y\right)$$

Rewrite the complete factored expression.

$$\frac{\left(30x-y\right)\left(30x+y\right)}{100}$$