Question

zapisz w jak najprostrzej postaci zad 13/83 a) (x+1)(x-2)+(x+2)(x-1)= b) (5k+n)(k-2n)-k(4k+n)= c) (4y+3)(y-2)-2y(4-2y)= d) -(3c-2)(c-1)-c(c-2)= e) 2(3a2-1)-(a+2)(a+2)= f) 5x2(x2+1)-(x2-2)(x2+3)=

Answer 1

A).(x+1)(x-2)+(x+2)(x-1) = x²-2x+x-2+x²-x+2x-2 = 2x²-4
b).(5k+n)(k-2n)-k(4k+n) = 5k²-10kn+kn-2n²-4k²-kn = k²-10kn-2n²
c).(4y+3)(y-2)-2y(4-2y) = 4y²-8y+3y-6-8y+4y² = 8y²-13y-6
d).-(3c-2)(c-1)-c(c-2) = -(3c²-3c-2c+2)-c²+2c = -(3c²-5c+2)-c²+2c =
= -3c²+5c-2-c²+2c = -4c²+7c-2
e).2(3a²-1)-(a+2)(a+2) = 6a²-2-(a+2)² = 6a²-2-(a²+4a+4) = 6a²-2-a²-4a-4 =
= 5a²-4a-6
f).5x²(x²+1)-(x²-2)(x²+3) = 5x⁴+5x²-(x⁴+3x²-2x²-6) = 5x⁴+5x²-(x⁴+x²-6) =
= 5x⁴+5x²-x⁴-x²²+6 = 4x⁴+4x²+6