Solve a^2/121-25b^2/144

$$\frac { a ^ { 2 } } { 121 } - \frac { 25 b ^ { 2 } } { 144 }$$

Factor

$$\frac{\left(12a-55b\right)\left(12a+55b\right)}{17424}$$

Solution Steps

Factor out \frac{1}{17424}.

$$\frac{144a^{2}-3025b^{2}}{17424}$$

Consider 144a^{2}-3025b^{2}. Rewrite 144a^{2}-3025b^{2} as \left(12a\right)^{2}-\left(55b\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(12a-55b\right)\left(12a+55b\right)$$

Rewrite the complete factored expression.

$$\frac{\left(12a-55b\right)\left(12a+55b\right)}{17424}$$

Evaluate

$$\frac{a^{2}}{121}-\frac{25b^{2}}{144}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 121 and 144 is 17424. Multiply \frac{a^{2}}{121} times \frac{144}{144}. Multiply \frac{25b^{2}}{144} times \frac{121}{121}.

$$\frac{144a^{2}}{17424}-\frac{121\times 25b^{2}}{17424}$$

Since \frac{144a^{2}}{17424} and \frac{121\times 25b^{2}}{17424} have the same denominator, subtract them by subtracting their numerators.

$$\frac{144a^{2}-121\times 25b^{2}}{17424}$$

Do the multiplications in 144a^{2}-121\times 25b^{2}.

$$\frac{144a^{2}-3025b^{2}}{17424}$$