Question
Evaluate: $\left(3 \mathrm{x}-\frac{1}{2 \mathrm{y}}\right)\left(3 \mathrm{x}+\frac{1}{2 \mathrm{y}}\right)$
✓
Answer
$ \left(3 x-\frac{1}{2 y}\right)\left(3 x+\frac{1}{2 y}\right)$
$ =3 x\left(3 x+\frac{1}{2 y}\right)-\frac{1}{2 y}\left(3 x+\frac{1}{2 y}\right)$
$ =9 x^2+\frac{3 x}{2 y}-\frac{3 x}{2 y}-\frac{1}{4 y^2}$
$ =9 x^2-\frac{1}{4 y^2}$
$ =3 x\left(3 x+\frac{1}{2 y}\right)-\frac{1}{2 y}\left(3 x+\frac{1}{2 y}\right)$
$ =9 x^2+\frac{3 x}{2 y}-\frac{3 x}{2 y}-\frac{1}{4 y^2}$
$ =9 x^2-\frac{1}{4 y^2}$
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