1. (x+y)(x-y) 2. (x+2)(y-6) 3. (4-a)(5-b) 4. (a-2)(3-a) 5. (2x-1)(3+4x) 6. (3b-7)(1+7b) 7. (5+3x)(2x-7) 8. (2a+3)(5+6a) 9. (1+8b)(6b-1) 10. (-2-a)(b+7) 11. (-5-n)(2x+3) 12. (-3-t)(4t-9) 13. (2a+7)(-3-a) 14. (a+b)(4a-5b) 15. (2x-4y)(x-y) 16. (-6-v)(2v-5) 17. (4u+v)(3v-u) 18. (-v-8u)(5v-u) 19. (2b-7)(-b+6) 20. (5t+3)(-t-7) 21. (-z-6)(4z-3)

Решение:

Необходимо раскрыть скобки и привести подобные слагаемые в каждом выражении.

1. \( (x+y)(x-y) = x^2 - y^2 \)
2. \( (x+2)(y-6) = xy - 6x + 2y - 12 \)
3. \( (4-a)(5-b) = 20 - 4b - 5a + ab \)
4. \( (a-2)(3-a) = 3a - a^2 - 6 + 2a = -a^2 + 5a - 6 \)
5. \( (2x-1)(3+4x) = 6x + 8x^2 - 3 - 4x = 8x^2 + 2x - 3 \)
6. \( (3b-7)(1+7b) = 3b + 21b^2 - 7 - 49b = 21b^2 - 46b - 7 \)
7. \( (5+3x)(2x-7) = 10x - 35 + 6x^2 - 21x = 6x^2 - 11x - 35 \)
8. \( (2a+3)(5+6a) = 10a + 12a^2 + 15 + 18a = 12a^2 + 28a + 15 \)
9. \( (1+8b)(6b-1) = 6b - 1 + 48b^2 - 8b = 48b^2 - 2b - 1 \)
10. \( (-2-a)(b+7) = -2b - 14 - ab - 7a \)
11. \( (-5-n)(2x+3) = -10x - 15 - 2nx - 3n \)
12. \( (-3-t)(4t-9) = -12t + 27 - 4t^2 + 9t = -4t^2 - 3t + 27 \)
13. \( (2a+7)(-3-a) = -6a - 2a^2 - 21 - 7a = -2a^2 - 13a - 21 \)
14. \( (a+b)(4a-5b) = 4a^2 - 5ab + 4ab - 5b^2 = 4a^2 - ab - 5b^2 \)
15. \( (2x-4y)(x-y) = 2x^2 - 2xy - 4xy + 4y^2 = 2x^2 - 6xy + 4y^2 \)
16. \( (-6-v)(2v-5) = -12v + 30 - 2v^2 + 5v = -2v^2 - 7v + 30 \)
17. \( (4u+v)(3v-u) = 12uv - 4u^2 + 3v^2 - uv = -4u^2 + 11uv + 3v^2 \)
18. \( (-v-8u)(5v-u) = -5v^2 + uv - 40uv + 8u^2 = 8u^2 - 39uv - 5v^2 \)
19. \( (2b-7)(-b+6) = -2b^2 + 12b + 7b - 42 = -2b^2 + 19b - 42 \)
20. \( (5t+3)(-t-7) = -5t^2 - 35t - 3t - 21 = -5t^2 - 38t - 21 \)
21. \( (-z-6)(4z-3) = -4z^2 + 3z - 24z + 18 = -4z^2 - 21z + 18 \)

Ответ:

1. \( x^2 - y^2 \)
2. \( xy - 6x + 2y - 12 \)
3. \( 20 - 4b - 5a + ab \)
4. \( -a^2 + 5a - 6 \)
5. \( 8x^2 + 2x - 3 \)
6. \( 21b^2 - 46b - 7 \)
7. \( 6x^2 - 11x - 35 \)
8. \( 12a^2 + 28a + 15 \)
9. \( 48b^2 - 2b - 1 \)
10. \( -2b - 14 - ab - 7a \)
11. \( -10x - 15 - 2nx - 3n \)
12. \( -4t^2 - 3t + 27 \)
13. \( -2a^2 - 13a - 21 \)
14. \( 4a^2 - ab - 5b^2 \)
15. \( 2x^2 - 6xy + 4y^2 \)
16. \( -2v^2 - 7v + 30 \)
17. \( -4u^2 + 11uv + 3v^2 \)
18. \( 8u^2 - 39uv - 5v^2 \)
19. \( -2b^2 + 19b - 42 \)
20. \( -5t^2 - 38t - 21 \)
21. \( -4z^2 - 21z + 18 \)