A) \[\frac{9}{16}{{a}^{2}}-\frac{4}{9}{{b}^{2}}\]
B) \[\frac{9}{16}{{a}^{2}}-\frac{6}{12}{{b}^{2}}\]
C) \[\frac{9}{16}{{a}^{2}}-\frac{6}{12}{{b}^{2}}-\frac{6}{12}{{b}^{2}}-\frac{4}{9}ab\]
D) \[\frac{6}{12}{{a}^{2}}-\frac{9}{16}{{b}^{2}}\]
Correct Answer: A
Solution :
\[\left( \frac{3a}{4}-\frac{2b}{3} \right)\left( \frac{3a}{4}+\frac{2b}{3} \right)\] \[=\frac{9}{16}{{a}^{2}}+\left( \frac{3a}{4} \right)\left( \frac{2b}{3} \right)-\left( \frac{2b}{3} \right)\left( \frac{3a}{4} \right)-\frac{4}{9}{{b}^{2}}\] \[=\frac{9}{16}{{a}^{2}}-\frac{4}{9}{{b}^{2}}\]
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