Let's solve these multiplication problems step by step:
(5x+6)(2x-9)+4 = 5x * 2x + 5x * -9 + 6 * 2x + 6 * -9 + 4 = 10x^2 - 45x + 12x - 54 + 4 = 10x^2 - 33x - 50
(6x-7)(5x+2)-9 = 6x * 5x + 6x * 2 - 7 * 5x - 7 * 2 - 9 = 30x^2 + 12x - 35x - 14 - 9 = 30x^2 - 23x - 23
(9x+8)(2x-9)+4 = 9x * 2x + 9x * -9 + 8 * 2x + 8 * -9 + 4 = 18x^2 - 81x + 16x - 72 + 4 = 18x^2 - 65x - 68
(5x+6)(2x-9)+9 = 5x * 2x + 5x * -9 + 6 * 2x + 6 * -9 + 9 = 10x^2 - 45x + 12x - 54 + 9 = 10x^2 - 33x - 45
(6x-7)(5x-2)+8 = 6x * 5x + 6x * -2 - 7 * 5x - 7 * -2 + 8 = 30x^2 - 12x - 35x + 14 + 8 = 30x^2 - 47x + 22
(2x+8)(2x+9)+5 = 2x * 2x + 2x * 9 + 8 * 2x + 8 * 9 + 5 = 4x^2 + 18x + 16x + 72 + 5 = 4x^2 + 34x + 77
(2x+8)(3x+9)-5 = 2x * 3x + 2x * 9 + 8 * 3x + 8 * 9 - 5 = 6x^2 + 18x + 24x + 72 - 5 = 6x^2 + 42x + 67
(x^2-5x+9)(5x^2+6x+2) = 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
(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
(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 - 44a^3 - 12a^2 - 16a - 3
(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 - 35a^2 - 35a - 6
(2y+6x)(8a-6y)+7 = 2y * 8a + 2y * (-6y) + 6x * 8a + 6x * (-6y) + 7 = 16ay - 12y^2 + 48ax - 36xy + 7
(2y+6x)(3a-8y)-7 = 2y * 3a + 2y * (-8y) + 6x * 3a + 6x * (-8y) - 7 = 6ay - 16y^2 + 18ax - 48xy - 7
(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
(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
(-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
(-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
(8a-3)(6x-1)-6x = 8a * 6x + 8a * (-1) - 3 * 6x - 3 * (-1) - 6x = 48ax - 8a - 18x + 3 - 6x = 48ax - 24x - 8a - 3
(8a-3)(-6x-5)+6x = 8a * (-6x) + 8a * (-5) - 3 * (-6x) - 3 * (-5) + 6x = -48ax - 40a + 18x + 15 + 6x = -48ax + 24x - 40a + 15
(-9a-3)(5x-1)-8x+9a = (-9a) * 5x + (-9a) * (-1) - 3 * 5x - 3 * (-1) - 8x + 9a = -45ax + 9a + 15x - 3 + 9a - 8x = -45ax + 15x + 18a - 3
