47. Simplify (a) $$ (2 x+2)(2 x-2) $$ and (b) $$ \left(5 x^{2}+9\right)\left(5 x^{2}-9\right) $$

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**(a) Simplify $$ (2x+2)(2x-2) $$:**

1. Recognize that the expression is in the form $$ (A+B)(A-B) $$ where $$ A = 2x $$ and $$ B = 2 $$.
2. Use the difference of squares formula:  
   $$
   (A+B)(A-B) = A^2 - B^2
   $$
3. Substitute the values of $$ A $$ and $$ B $$:
   $$
   (2x)^2 - 2^2 = 4x^2 - 4
   $$

**(b) Simplify $$ \left(5x^2+9\right)\left(5x^2-9\right) $$:**

1. Recognize that this expression is also in the form $$ (A+B)(A-B) $$ where $$ A = 5x^2 $$ and $$ B = 9 $$.
2. Use the difference of squares formula:
   $$
   (A+B)(A-B) = A^2 - B^2
   $$
3. Substitute the values of $$ A $$ and $$ B $$:
   $$
   (5x^2)^2 - 9^2 = 25x^4 - 81
   $$

**Final Answers:**

- **(a)** $$ 4x^2 - 4 $$
- **(b)** $$ 25x^4 - 81 $$
**(a)** $$ 4x^2 - 4 $$ **(b)** $$ 25x^4 - 81 $$

Simplify (a) and (b)

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