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(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-x-2+x²+x-2=2x²-4
b) (5k+n)(k-2n)-k(4k+n)=5k²-9kn-2n²
c) (4y+3)(y-2)-2y(4-2y)=4y²-5y-6-8y+4y²=8y²-13y-6
d) -(3c-2)(c-1)-c(c-2)=-3c²+5c-2-c²+2c=-4c²+7c-2
e) 2(3a2-1)-(a+2)(a+2)=6a²-2-a²+4a+4=5a²+4a+2
f) 5x2(x2+1)-(x2-2)(x2+3)=5x⁴+5x²-x⁴+x²+6=4x⁴+6x²+6

Answer 2

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+nk-2n²-4k²-nk=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=-4c²+7c-2
e) 2(3a²-1)-(a+2)(a+2)=6a²-2-a²-2a-2a-4=5a²-4a-6
f) 5x²(x²+1)-(x²-2)(x²+3)=5x⁴+5x²-x⁴-3x²+2x²+6=4x⁴+4x²+6

Answer 3

A) (x+1)(x-2)+(x+2)(x-1)=x²-2x+x-2+x²-x+2x-2=2x²-4=2(x²-2)
b) (5k+n)(k-2n)-k(4k+n)=5k²-10kn+kn-2n²-(4k²+kn)=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=-4c²+7c-2
e) 2(3a2-1)-(a+2)(a+2)=6a²-2-a²-4a-4=5a²-4a-6
f) 5x2(x2+1)-(x2-2)(x2+3)=5x⁴+5x²-x⁴-3x²+2x²+6=4x⁴+4x²+6=4x²(x²+1)+6=
=2[2x²(x²+1)+3]