If the highest common factor (HCF) of *x* and *y* is 15, then the HCF of $$36x^2 - 81y^2$$ and $$81x^2 - 9y^2$$ is divisible by _______.

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**Solution:**

1. Given expressions:
   - $$36x^2 - 81y^2$$
   - $$81x^2 - 9y^2$$

2. Factor each expression:
   - $$36x^2 - 81y^2 = 9(4x^2 - 9y^2)$$
   - $$81x^2 - 9y^2 = 9(9x^2 - y^2)$$

3. The common factor from both expressions is at least 9.

4. Since the HCF of *x* and *y* is 15, both *x* and *y* are divisible by 15.

5. Substitute *x = 15a* and *y = 15b*, where HCF of *a* and *b* is 1.

6. Then the expressions become:
   - $$36(15a)^2 - 81(15b)^2 = 36 	imes 225 a^2 - 81 	imes 225 b^2 = 225 (36a^2 - 81b^2)$$
   - $$81(15a)^2 - 9(15b)^2 = 81 	imes 225 a^2 - 9 	imes 225 b^2 = 225 (81a^2 - 9b^2)$$

7. The factor 225 (= 15^2) is common in both expressions.

8. From earlier, the common factor 9 was factored out, so the total common factor includes 9 and 15.

9. Therefore, the HCF of the two expressions is divisible by:
   $$15 	imes 9 = 135$$

**Answer:** 135

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