Solve 1/36a^2b^2-16/49b^2c^2

$$\frac { 1 } { 36 } a ^ { 2 } b ^ { 2 } - \frac { 16 } { 49 } b ^ { 2 } c ^ { 2 }$$

Factor

$$\frac{\left(7a-24c\right)\left(7a+24c\right)b^{2}}{1764}$$

Solution Steps

Factor out \frac{1}{1764}.

$$\frac{49a^{2}b^{2}-576b^{2}c^{2}}{1764}$$

Consider 49a^{2}b^{2}-576b^{2}c^{2}. Factor out b^{2}.

$$b^{2}\left(49a^{2}-576c^{2}\right)$$

Consider 49a^{2}-576c^{2}. Rewrite 49a^{2}-576c^{2} as \left(7a\right)^{2}-\left(24c\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(7a-24c\right)\left(7a+24c\right)$$

Rewrite the complete factored expression.

$$\frac{b^{2}\left(7a-24c\right)\left(7a+24c\right)}{1764}$$

Evaluate

$$\frac{\left(ab\right)^{2}}{36}-\frac{16\left(bc\right)^{2}}{49}$$