Zadanie 1
[tex]a)\\(x+2)(y+1) = xy + x + 2y + 2\\\\b)\\(2a +1)(3-b) = 6a - 2ab + 3 - b\\\\c)\\(a -1)(a^2-b^2)= a^3 - ab^2 - a^2 + b^2\\\\d)\\(2x-1)(y-3)=2xy -6x-y+3\\\\[/tex]
Zadanie 2
[tex]a)\\(x+1)(x+2) = x^2 + 2x + x + 2 = x^2 + 3x +2\\\\b)\\(3a+4)(a-5) = 3a^2 - 15a + 4a - 20 = 3a^2 + 11a -20\\\\c)\\(2t+1)(1-3t)=2t -6t^2 + 1 - 3t = -t - 6t^2 + 1 = -6t^2 -t + t\\\\d)\\(3ab-7)(3-7ab) = 9ab - 21a^2b^2 - 21 + 49ab = 58ab - 21a^2b^2 - 21\\\\e)\\(-x+y)(5x+6y) = -5x^2 - 6xy + 5xy + 6y^2 = -5x^2 - xy + 6y^2\\\\f)\\(x+5)(7x-y) = 7x^2 - xy + 35x - 5y = -7x^2 + 34xy -5y^2\\\\g)\\(2x-y)(x+y) = 2x^2 + 2xy - xy - y^2 = 2x^2 + xy - y^2\\\\[/tex]
[tex]h)\\(ab-a)(2ab+6a)=2a^2b^2 + 6a^2b - 2a^2b - 6a^2 = 2a^2b^2 + 4a^2b - 6a^2[/tex]
Zadanie 3
[tex]a)\\(t+1)(t^2+2t+3)=1^3+2t^2+3t+t^2+2t+3=t^3+3t^2+5t+3\\\\b)\\(p-2)(3p^2 -5p +1) = 3p^3 - 5p^2 + p = 6p^2 + 10p -2 = 3p^3 - 11p^2 + 11p -2\\\\c)\\(2m-1)(-2m^2 +3m -5) = -4m^3 + 6m^2 - 10m + 2m^2 - 3m + 5 = -4m^3 + 8m^2 - 13m + 5\\\\d)\\(4-5w)(3w^2-w-2) = 12w^2 -4w-8-15w^3+5w^2+10w=-15w^3+17w^2+6w-8[/tex]
Zadanie 4
[tex]a)\\P = (x+5)(x-2) = x^2 - 2x + 5x - 10 = x^2 + 3x-10\\\\b)\\P = (x+3)(x-3) : 2 = (x^2 - 3x + 3x -9) : 2 = (x^2 -9) : 2 \\\\c)\\P = (x+x+2)(x+1) : 2 = 2(x+1)(x+1) : 2 = (x + 1)(x+1) = (x+1)^2 = x^2 + 2x +1[/tex]
Zadanie 5
[tex]a)\\(x+3)^2=x^2+2x * 3 + 3^2 = x^2+6x+9\\\\b)\\ (a-2)^2 = a^2 - 2a * 2 + 2^2 = a^2 - 4a + 4\\\\c)\\(2x+5)^2 = (2x)^2+2 * 2x * 5 + 5^2 = 4x^2 + 20x + 25[/tex]
