Question

16.Calculaţi:
a) (x - 1)(x² + x + 1);
c) (x - x + 1)(x² + x + 1);
b) (x + 1)(x - x + 1);
d) (x - 1)(x + 1)(x-2)(x + 2).​

Answer 1

a)(x-1)(x²+x+1)=x³-1³=x³-1

c)(x-x+1)(x²+x+1)=x(x²+x+1)-x(x²+x+1)+1(x²+x+1)=x³+x²+x-x³-x²-x+x²+x+1=x²+x+1

b)(x+1)(x-x+1)=x(x-x+1)+1(x-x+1)=x²-x²+x+x-x+1=x+1

d)(x-1)(x+1)(x-2)(x+2)=(x²-1)(x-2)(x+2)=(x²-1)(x²-4)=x⁴-4x²-x²+4=x⁴-5x²+4