Question

Zapisz w jak najprostszej postaci: 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(3a^2-1) -(a+2)(a+2) f) 5x^2(x^2+1)-(x^2-2)(x^2+3)

Answer 1

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}-2kn+kn-2n^{2}--4k^{2}-kn=k^{2}-10kn-2n^{2}

c) (4y+3) (y-2)-2y(4-2y)=8y^{2}-13y-6

d) -(3c-2) (c-1)-c(c_2)=-(3c^{2}-(3c-2c+2)-c^{2}+2c=-3c^{2}+3c+2c-2-c^{2}+2c=-4c^{2}+7c-2

e) 2(3a^2-1) -(a+2)(a+2)=6a^{2}-2-(a^{2}+4a+4)=6a^{2}-2-a^{2}-4a-4=5a^{2}-4a-6

f) 5x^2(x^2+1)-(x^2-2)(x^2+3)=5x^{4}+5x^{2}-(x^{4}+x^{2}-6)=5x^{4}+5x^{2}-x^{4}-x^{2}+6=4x^{4}+4x^{2}+6