[tex]Zadanie 13\\\\a)\\(x + 1)(x + 2)(x + 3)\\(x^2 + 2x + x + 2)(x +3)\\(x^2 + 3x + 2)(x +3)\\x^3 + 3x^2 + 3x^2 + 9x + 2x + 6\\x^3 + 6x^2 + 11x + 6\\\\b)\\(x-2)(x+5)(2x-1)\\(x^2 + 5x - 2x -10)(2x-1)\\(x^2 + 3x -10)(2x -1)\\2x^3 -x^2 + 6x^2 -3x -20x + 10\\2x^3 + 5x^2 - 23x + 10\\\\c)\\(x-4)(x+1)^2\\(x-4)(x^2 +2x +1)\\x^3 + 2x^2 + x -4x^2 -8x - 4\\x^3 - 2x^2 - 7x - 4\\\\d) \\(2x -3)^2(x+2)\\(4x^2 - 12x + 9)(x+2) \\4x^3 +8x^2 - 12x^2 - 24x + 9x + 18\\4x^3 - 4x^2 - 15x + 18\\\\\\\\\\[/tex][tex]\\Zadanie 14\\\\a)\\ (x+1)(x-2)+(x+2)(x-1) = x^2 - 2x + x - 2 + x^2 - x + 2x - 2 = 2x^2 - 4\\\\b)\\(5k+n)(k-2n)-k(4k +n) = 5k^2 - 10kn + kn - 2n^2 = 4k^2 - kn = k^2 - 10kn - 2n^2\\\\c)\\(4y+3)(y-2)-2y(4-2y) = 4y^2 - 8y + 3y - 6 - 8y + 4y^2 = 8y^2 - 13y - 6\\\\\\d)\\-(3c-2)(c-1)-c(c-2) = -(3c^2) - 3c - 2c +2)-c^2 +2c = -(3c^2 - 5c +2) - c^2 + 2c= -3c^2 + 5c - 2 - c^2 + 2c=-4c^2 + 7c -2\\\\[/tex][tex]e)\\2(3a^2 -1) - (a+2)(a+2) = 6a^2 - 2 - (a+2)^2 = 6a^2 -2 - (a^2 + 4a + 4)= 6a^2 -2-a^2 - 4a -4 = 5a^2 - 6 - 4a=5a^2-4a-6\\\\f)\\5x^2(x^2 +1)-(x^2-2)(x^2+3) = 5x^4 + 5x^2 - (x^4 + 3x^2 - 2x^2 -6) = 5x^4 + 5x^2 - (x^4 + x^2 - 6) = 5x^4 + 5x^2 - x^4 - x^2 +6 = 4x^4 + 4x^2 + 6[/tex]
