(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

I'll provide the steps for simplifying each expression:

1. (5x+6)(2x-9)+4 Multiply each term of the first expression by each term of the second expression and then add them together to get: 10x^2 - 45x + 12x - 54 + 4 Combine like terms: 10x^2 - 33x - 50

2. (6x-7)(5x+2)-9 Multiply each term of the first expression by each term of the second expression and then subtract 9 to get: 30x^2 + 12x - 35x - 14 - 9 Combine like terms: 30x^2 - 23x - 23

3. (9x+8)(2x-9)+4 Multiply each term of the first expression by each term of the second expression and then add them together to get: 18x^2 - 81x + 16x - 72 + 4 Combine like terms: 18x^2 - 65x - 68

4. (5x+6)(2x-9)+9 Multiply each term of the first expression by each term of the second expression and then add 9 to get: 10x^2 - 45x + 12x - 54 + 9 Combine like terms: 10x^2 - 33x - 45

5. (6x-7)(5x-2)+8 Multiply each term of the first expression by each term of the second expression and then add 8 to get: 30x^2 - 12x - 35x + 14 + 8 Combine like terms: 30x^2 - 47x + 22

6. (2x+8)(2x+9)+5 Multiply each term of the first expression by each term of the second expression and then add 5 to get: 4x^2 + 18x + 16x + 72 + 5 Combine like terms: 4x^2 + 34x + 77

7. (2x+8)(3x+9)-5 Multiply each term of the first expression by each term of the second expression and then subtract 5 to get: 6x^2 + 27x + 24x + 72 - 5 Combine like terms: 6x^2 + 51x + 67

8. (x^2-5x+9)(5x^2+6x+2) Multiply each term of the first expression by each term of the second expression to get: 5x^4 - 25x^3 + 45x^2 + 6x^3 - 30x^2 + 54x + 2x^2 - 10x + 18 Combine like terms: 5x^4 - 19x^3 + 47x^2 + 44x + 18

9. (x^2-5x+9)(x^2-6x+2) Multiply each term of the first expression by each term of the second expression to get: x^4 - 6x^3 + 2x^2 - 5x^3 + 30x^2 - 10x + 9x^2 - 54x + 18 Combine like terms: x^4 - 11x^3 + 41x^2 - 64x + 18

10. (2a^2+6a+1)(2a-8a^2-3) Multiply each term of the first expression by each term of the second expression to get: 4a^3 - 16a^4 - 6a^2 + 12a^2 - 48a^3 - 18a + 2a - 8a^2 - 3 Combine like terms: -16a^4 - 44a^3 - 12a^2 - 16a - 3

11. (2a^2+6a+1)(a-5a^2-6) Multiply each term of the first expression by each term of the second expression to get: 2a^3 - 10a^4 - 12a^2 + 6a^2 - 30a^3 - 36a + a - 5a^2 - 6 Combine like terms: -10a^4 - 28a^3 - 11a^2 - 35a - 6

12. (2y+6x)(8a-6y)+7 Multiply each term of the first expression by each term of the second expression and then add 7 to get: 16ay - 12y^2 + 48ax - 36xy + 7 Combine like terms: -12y^2 - 36xy + 48ax + 16ay + 7

13. (2y+6x)(3a-8y)-7 Multiply each term of the first expression by each term of the second expression and then subtract 7 to get: 6ay - 16y^2 + 18ax - 48xy - 7 Combine like terms: -16y^2 - 48xy + 18ax + 6ay - 7

14. (2k+6y)(5k-8y)+12k Multiply each term of the first expression by each term of the second expression and then add 12k to get: 10k^2 - 16ky + 30ky - 48y^2 + 12k Combine like terms: 10k^2 + 14ky - 48y^2 + 12k

15. (2k+6y)(8k-5y)-12k Multiply each term of the first expression by each term of the second expression and then subtract 12k to get: 16k^2 - 10ky + 48ky - 30y^2 - 12k Combine like terms: 16k^2 + 38ky - 30y^2 - 12k

16. (-7x+4y)(2x-3y)+13 Multiply each term of the first expression by each term of the second expression and then add 13 to get: -14x^2 + 21xy + 8xy - 12y^2 + 13 Combine like terms: -14x^2 + 29xy - 12y^2 + 13

17. (-7x+4y)(9x-2y)-13 Multiply each term of the first expression by each term of the second expression and then subtract 13 to get: -63x^2 + 14xy + 36xy - 8y^2 - 13 Combine like terms: -63x^2 + 50xy - 8y^2 - 13

18. (8a-3)(6x-1)-6x Multiply each term of the first expression by each term of the second expression and then subtract 6x to get: 48ax - 8a - 18x + 3 - 6x Combine like terms: 48ax - 24x - 8a + 3

19. (8a-3)(-6x-5)+6x Multiply each term of the first expression by each term of the second expression and then add 6x to get: -48ax - 40a + 18x + 15 + 6x Combine like terms: -48ax + 24x - 40a + 15

20. (-9a-3)(5x-1)-8x+9a Multiply each term of the first expression by each term of the second expression and then subtract 8x and add 9a to get: -45ax + 9a + 15x - 3 - 8x + 9a Combine like terms: -45ax + 24x + 18a - 3+!