Умножение многлечленов (5x+6)(2x-9)+4 (6x-7)(5x+2)-9 (9x+8)(2x-9)+4 (5x+6)(2x-9)+9 (6x-7)(5x-2)+8 (2x+8)(2x+9)+5 (2x+8)(3x+9)-5 (x^{2}-5x+9)(5x^{2}+6x+2) (x^{2}-5x+9)(x^{2}-6x+2) (2a^{2}+6a+1)(2a-8a^{2}-3) (2a^{2}+6a+1)(a-5a^{2}-6) (2y+6x)(8a-6y)+7 (2y+6x)(3a-8y)-7 (2k+6y)(5k-8y)+12k (2k+6y)(8k-5y)-12k (-7x+4y)(2x-3y)+13 (-7x+4y)(9x-2y)-13 (8a-3)(6x-1)-6x (8a-3)(-6x-5)+6x (-9a-3)(5x-1)-8x+9a

To multiply polynomials, we can use the distributive property. We'll go through each example step by step:

1. (5x+6)(2x-9)+4

Using the FOIL method (First, Outer, Inner, Last): = (5x * 2x) + (5x * -9) + (6 * 2x) + (6 * -9) + 4 = 10x^2 - 45x + 12x - 54 + 4 = 10x^2 - 33x - 50

2. (6x-7)(5x+2)-9

= (6x * 5x) + (6x * 2) + (-7 * 5x) + (-7 * 2) - 9 = 30x^2 + 12x - 35x - 14 - 9 = 30x^2 - 23x - 23

3. (9x+8)(2x-9)+4

= (9x * 2x) + (9x * -9) + (8 * 2x) + (8 * -9) + 4 = 18x^2 - 81x + 16x - 72 + 4 = 18x^2 - 65x - 68

4. (5x+6)(2x-9)+9

= (5x * 2x) + (5x * -9) + (6 * 2x) + (6 * -9) + 9 = 10x^2 - 45x + 12x - 54 + 9 = 10x^2 - 33x - 45

5. (6x-7)(5x-2)+8

= (6x * 5x) + (6x * -2) + (-7 * 5x) + (-7 * -2) + 8 = 30x^2 - 12x - 35x + 14 + 8 = 30x^2 - 47x + 22

6. (2x+8)(2x+9)+5

= (2x * 2x) + (2x * 9) + (8 * 2x) + (8 * 9) + 5 = 4x^2 + 18x + 16x + 72 + 5 = 4x^2 + 34x + 77

7. (2x+8)(3x+9)-5

= (2x * 3x) + (2x * 9) + (8 * 3x) + (8 * 9) - 5 = 6x^2 + 18x + 24x + 72 - 5 = 6x^2 + 42x + 67

8. (x^2-5x+9)(5x^2+6x+2)

Using the distributive property with each term of the first polynomial: = (x^2 * 5x^2) + (x^2 * 6x) + (x^2 * 2) + (-5x * 5x^2) + (-5x * 6x) + (-5x * 2) + (9 * 5x^2) + (9 * 6x) + (9 * 2) = 5x^4 + 6x^3 + 2x^2 - 25x^3 - 30x^2 - 10x + 45x^2 + 54x + 18 = 5x^4 - 19x^3 + 17x^2 + 44x + 18

9. (x^2-5x+9)(x^2-6x+2)

= (x^2 * x^2) + (x^2 * -6x) + (x^2 * 2) + (-5x * x^2) + (-5x * -6x) + (-5x * 2) + (9 * x^2) + (9 * -6x) + (9 * 2) = x^4 - 6x^3 + 2x^2 - 5x^3 + 30x^2 - 10x + 9x^2 - 54x + 18 = x^4 - 11x^3 + 41x^2 - 64x + 18

10. (2a^2+6a+1)(2a-8a^2-3)

= (2a^2 * 2a) + (2a^2 * -8a^2) + (2a^2 * -3) + (6a * 2a) + (6a * -8a^2) + (6a * -3) + (1 * 2a) + (1 * -8a^2) + (1 * -3) = 4a^3 - 16a^4 - 6a^2 + 12a^2 - 48a^3 - 18a + 2a - 8a^2 - 3 = -16a^4 - 32a^3 - 2a^2 - 16a

11. (2a^2+6a+1)(a-5a^2-6)

= (2a^2 * a) + (2a^2 * -5a^2) + (2a^2 * -6) + (6a * a) + (6a * -5a^2) + (6a * -6) + (1 * a) + (1 * -5a^2) + (1 * -6) = 2a^3 - 10a^4 - 12a^2 + 6a^2 - 30a^3 - 36a + a - 5a^2 - 6 = -10a^4 - 28a^3 - 11a^2 - 35a

12. (2y+6x)(8a-6y)+7

= (2y * 8a) + (2y * -6y) + (6x * 8a) + (6x * -6y) + 7 = 16ay - 12y^2 + 48ax - 36xy + 7

13. (2y+6x)(3a-8y)-7

= (2y * 3a) + (2y * -8y) + (6x * 3a) + (6x * -8y) - 7 = 6ay - 16y^2 + 18ax - 48xy - 7

14. (2k+6y)(5k-8y)+12k

= (2k * 5k) + (2k * -8y) + (6y * 5k) + (6y * -8y) + 12k = 10k^2 - 16ky + 30ky - 48y^2 + 12k = 10k^2 + 14ky - 48y^2 + 12k

15. (2k+6y)(8k-5y)-12k

= (2k * 8k) + (2k * -5y) + (6y * 8k) + (6y * -5y) - 12k = 16k^2 - 10ky + 48ky - 30y^2 - 12k = 16k^2 + 38ky - 30y^2 - 12k

16. (-7x+4y)(2x-3y)+13

= (-7x * 2x) + (-7x * -3y) + (4y * 2x) + (4y * -3y) + 13 = -14x^2 + 21xy + 8xy - 12y^2 + 13 = -14x^2 + 29xy - 12y^2 + 13

17. (-7x+4y)(9x-2y)-13

= (-7x * 9x) + (-7x * -2y) + (4y * 9x) + (4y * -2y) - 13 = -63x^2 + 14xy + 36xy - 8y^2 - 13 = -63x^2 + 50xy - 8y^2 - 13

18. (8a-3)(6x-1)-6x

= (8a * 6x) + (8a * -1) + (-3 * 6x) + (-3 * -1) - 6x = 48ax - 8a - 18x + 3 - 6x = 48ax - 6x - 18x - 8a + 3 = 48ax - 24x - 8a + 3

19. (8a-3)(-6x-5)+6x

= (8a * -6x) + (8a * -5) + (-3 * -6x) + (-3 * -5) + 6x = -48ax - 40a + 18x + 15 + 6x = -48ax + 24x - 40a + 15

20. (-9a-3)(5x-1)-8x+9a

= (-9a * 5x) + (-9a * -1) + (-3 * 5x) + (-3 * -1) - 8x + 9a = -45ax + 9a + 15x - 3 - 8x + 9a = -45ax + 15x + 18a - 3