Разложите на множители: 1) x² - 25; 2) 36 - 16y²; 3) 4x² - 81y²; 4) 0,09t² - 121p²; 5) a²b² - 16/9; 6) a⁸ - x¹⁰; 7) 0,04b⁴ - a¹²; 8) 1,69y¹⁴ - 900z⁸; 9) -1 + 36a⁶b⁴; 10) 1/25 m⁶n⁴ - 9/16 a²b⁸.

Разложим на множители, используя формулу разности квадратов $$a^2 - b^2 = (a - b)(a + b)$$.

1. $$x^2 - 25 = (x - 5)(x + 5)$$

2. $$36 - 16y^2 = (6 - 4y)(6 + 4y)$$

3. $$4x^2 - 81y^2 = (2x - 9y)(2x + 9y)$$

4. $$0.09t^2 - 121p^2 = (0.3t - 11p)(0.3t + 11p)$$

5. $$a^2b^2 - \frac{16}{9} = (ab - \frac{4}{3})(ab + \frac{4}{3})$$

6. $$a^8 - x^{10} = (a^4 - x^5)(a^4 + x^5)$$

7. $$0.04b^4 - a^{12} = (0.2b^2 - a^6)(0.2b^2 + a^6)$$

8. $$1.69y^{14} - 900z^8 = (1.3y^7 - 30z^4)(1.3y^7 + 30z^4)$$

9. $$-1 + 36a^6b^4 = (6a^3b^2 - 1)(6a^3b^2 + 1)$$

10. $$\frac{1}{25}m^6n^4 - \frac{9}{16}a^2b^8 = (\frac{1}{5}m^3n^2 - \frac{3}{4}ab^4)(\frac{1}{5}m^3n^2 + \frac{3}{4}ab^4)$$

Ответы:

1. $$(x - 5)(x + 5)$$
2. $$(6 - 4y)(6 + 4y)$$
3. $$(2x - 9y)(2x + 9y)$$
4. $$(0.3t - 11p)(0.3t + 11p)$$
5. $$(ab - \frac{4}{3})(ab + \frac{4}{3})$$
6. $$(a^4 - x^5)(a^4 + x^5)$$
7. $$(0.2b^2 - a^6)(0.2b^2 + a^6)$$
8. $$(1.3y^7 - 30z^4)(1.3y^7 + 30z^4)$$
9. $$(6a^3b^2 - 1)(6a^3b^2 + 1)$$
10. $$(\frac{1}{5}m^3n^2 - \frac{3}{4}ab^4)(\frac{1}{5}m^3n^2 + \frac{3}{4}ab^4)$$