Question

1.Zapisz w jak najprostszej postaci:
a) (x+1)(x-2)+(x+2)(x-1)
b) (5k+n)(k-2n)-k(4k+n)

2.Zapisz w postaci sumy algebraicznej:
a) (x+1)(x+2)(x+3)
b) (x-2)(x+5)(2x-1)

Answer 1

A) (x+1)(x-2)+(x+2)(x-1) = x+1 * x-2 + x+2 * x-1 = x2-2 + x2-2 = 0
b) (5k+n)(k-2n)-k(4k+n) = 5k+n * k - 2n - 4k2+kn = 5k2 + kn -2n - 4k2+kn = k2 + 2kn -2n


a) (x+1)(x+2)(x+3) = x3+6
b) (x-2)(x+5)(2x-1) = x3+10

Answer 2

1.Zapisz w jak najprostszej postaci:
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)=5k²-10kn+kn-2n²-4k²+kn=
k²-8kn-2n²

2.Zapisz w postaci sumy algebraicznej:
a) (x+1)(x+2)(x+3)= (x²+2x+x+2)(x+3)=(x²+3x+2)(x+3)=x³+3x²+3x²+9x+2x+6=
= x³+6x²+11x+6
b) (x-2)(x+5)(2x-1)=(x²+5x-2x-10)(2x-1)=(x²+3x-10)(2x-1)=
=2x³-x²+6x²-3x-20x+10=2x³+5x²-23x+10