Odpowiedź:
Zad 1
2(3t+2)²-5(2t-3)(2t+3)-(t-7)²=
2(9t²+12t+4)-5(4t²-9)-(t²-14t+49)=
18t²+24t+8-20t²+45-t²+14t-49=
-3t²+38t+4
czyli odp.: D
Zad 2
a)
5a²-12ab+7b²-(4ab-10a²+3b²)=
5a²-12ab+7b²-4ab+10a²-3b²=
15a²-16ab+4b²
Wielomian jest 2 stopnia.
b)
3p(p+q)-20(5p-2q)-4q(3p+5q)=
3p²+3pq-100p+40q-12pq-20q²=
3p²-9pq-100p+40q-20q²
Wielomian jest 2 stopnia.
c)
2(x-2y)²+4(3x+2y)(3x-2y)-(4x-y)²=
2(x²-4xy+4y²)+4(9x²-4y²)-(16x²-8xy+y²)=
2x²-8xy+8y²+36x²-16y²-16x²+8xy-y²=
22x²-9y²
Wielomian 2 stopnia.
Zad 3
O=2(3x+2y)+x+y+2(x+y)+x+2y=6x+4y+2x+3y+2x+2y=10x+9y
P=(4x+3y)(2x+3y)-(x+y)(x+2y)=8x²+18xy+9y²-(x²+3xy+2y²)=8x²+18xy+9y²-x²-3xy-2y²=7x²+15xy+7y²
