Привет! Это классические задачи на формулу разности квадратов: $(a - b)(a + b) = a^2 - b^2$. Давай решим их по очереди.
### Столбец А
1. $(x - y)(x + y) = x^2 - y^2$
2. $(2x - 1)(2x + 1) = (2x)^2 - 1^2 = 4x^2 - 1$
3. $(8c + 9d)(8c - 9d) = (8c)^2 - (9d)^2 = 64c^2 - 81d^2$
4. $(4x + 3y)(3y - 4x) = (3y + 4x)(3y - 4x) = (3y)^2 - (4x)^2 = 9y^2 - 16x^2$
5. $(1 - 3k)(1 + 3k) = 1^2 - (3k)^2 = 1 - 9k^2$
6. $(a^2 - 3)(a^2 + 3) = (a^2)^2 - 3^2 = a^4 - 9$
7. $(y - a^2)(y + a^2) = y^2 - (a^2)^2 = y^2 - a^4$
8. $(b^3 - c)(b^3 + c) = (b^3)^2 - c^2 = b^6 - c^2$
9. $(\frac{1}{3}x - y)(\frac{1}{3}x + y) = (\frac{1}{3}x)^2 - y^2 = \frac{1}{9}x^2 - y^2$
10. $(m^2 - p^3)(m^2 + p^3) = (m^2)^2 - (p^3)^2 = m^4 - p^6$
11. $(2a - 3b)(2a + 3b) = (2a)^2 - (3b)^2 = 4a^2 - 9b^2$
12. $(10x - 6c)(10x + 6c) = (10x)^2 - (6c)^2 = 100x^2 - 36c^2$
13. $(5a^2 - 2x^3)(2x^3 + 5a^2) = (5a^2 - 2x^3)(5a^2 + 2x^3) = (5a^2)^2 - (2x^3)^2 = 25a^4 - 4x^6$
14. $(\frac{1}{4}x^2 + y^7)(\frac{1}{4}x^2 - y^7) = (\frac{1}{4}x^2)^2 - (y^7)^2 = \frac{1}{16}x^4 - y^{14}$
15. $(5a^8 - 6x^3)(6x^3 + 5a^8) = (5a^8 - 6x^3)(5a^8 + 6x^3) = (5a^8)^2 - (6x^3)^2 = 25a^{16} - 36x^6$
16. $(5x^2 + 2y^3)(5x^2 - 2y^3) = (5x^2)^2 - (2y^3)^2 = 25x^4 - 4y^6$
17. $(a^3 - b^2)(a^3 + b^2) = (a^3)^2 - (b^2)^2 = a^6 - b^4$
18. $(0,7x + y^2)(0,7x - y^2) = (0,7x)^2 - (y^2)^2 = 0,49x^2 - y^4$
19. $(0,4c + 0,8y^2)(0,8y^2 - 0,4c) = (0,8y^2 + 0,4c)(0,8y^2 - 0,4c) = (0,8y^2)^2 - (0,4c)^2 = 0,64y^4 - 0,16c^2$
20. $(0,4x^6 - 0,7y^9)(0,7y^9 + 0,4x^6) = (0,4x^6 - 0,7y^9)(0,4x^6 + 0,7y^9) = (0,4x^6)^2 - (0,7y^9)^2 = 0,16x^{12} - 0,49y^{18}$
### Столбец Б
1. $(p - q)(p + q) = p^2 - q^2$
2. $(7 + 3y)(7 - 3y) = 7^2 - (3y)^2 = 49 - 9y^2$
3. $(8b + 5a)(5a - 8b) = (5a + 8b)(5a - 8b) = (5a)^2 - (8b)^2 = 25a^2 - 64b^2$
4. $(5x - 10y)(5x + 10y) = (5x)^2 - (10y)^2 = 25x^2 - 100y^2$
5. $(4y + m)(m - 4y) = (m + 4y)(m - 4y) = m^2 - 16y^2$
6. $(x^2 + m)(m - x^2) = (m + x^2)(m - x^2) = m^2 - x^4$
7. $(a^2 - 4)(a^2 + 4) = (a^2)^2 - 4^2 = a^4 - 16$
8. $(x^3 - 2y^4)(x^3 + 2y^4) = (x^3)^2 - (2y^4)^2 = x^6 - 4y^8$
9. $(0,1a - b)(0,1a + b) = (0,1a)^2 - b^2 = 0,01a^2 - b^2$
10. $(\frac{3}{7} + 6a)(6a - \frac{3}{7}) = (6a + \frac{3}{7})(6a - \frac{3}{7}) = (6a)^2 - (\frac{3}{7})^2 = 36a^2 - \frac{9}{49}$
11. $(2y + 3z)(2y - 3z) = (2y)^2 - (3z)^2 = 4y^2 - 9z^2$
12. $(3a - 5)(5 + 3a) = (3a - 5)(3a + 5) = (3a)^2 - 5^2 = 9a^2 - 25$
13. $(2a + x^2)(2a - x^2) = (2a)^2 - (x^2)^2 = 4a^2 - x^4$
14. $(x^4 - a^5)(a^5 + x^4) = (x^4 - a^5)(x^4 + a^5) = (x^4)^2 - (a^5)^2 = x^8 - a^{10}$
15. $(\frac{1}{5}x^2 + y^3)(\frac{1}{5}x^2 - y^3) = (\frac{1}{5}x^2)^2 - (y^3)^2 = \frac{1}{25}x^4 - y^6$
16. $(a^4 - d^2)(d^2 + a^4) = (a^4 - d^2)(a^4 + d^2) = (a^4)^2 - (d^2)^2 = a^8 - d^4$
17. $(0,3a - b^3)(b^3 + 0,3a) = (0,3a - b^3)(0,3a + b^3) = (0,3a)^2 - (b^3)^2 = 0,09a^2 - b^6$
18. $(2x^5 - 3y^2)(2x^5 + 3y^2) = (2x^5)^2 - (3y^2)^2 = 4x^{10} - 9y^4$
19. $(0,6x + 0,9y^3)(0,9y^3 - 0,6x) = (0,9y^3 + 0,6x)(0,9y^3 - 0,6x) = (0,9y^3)^2 - (0,6x)^2 = 0,81y^6 - 0,36x^2$
20. $(m^4 - n^7)(n^7 + m^4) = (m^4 - n^7)(m^4 + n^7) = (m^4)^2 - (n^7)^2 = m^8 - n^{14}$
