Question

Zadanie z tematu. Zastosowanie wzorów skróconego mnożenia:

a) (2y + 5z) (2y-5z) -5z(y-5z) =
b) (3a+b)² - 2a (4a-b)=
c) (2a+3b)²-4a(a-2b)+(a+b)(a-9b)=
d) (5y-2z)(5y+2z)+4z(y+z)-25y²=
e) (x-1)²+17-(x+2)²+5(x-2)=
f) 6x(x-3)+(2x+3)²-10x(x+1)+16x=
g) 5a(3a-b)-(2a-b)²+4b(a-2b)+3b(3b-a)=

Answer 1

A) (2y + 5z) (2y-5z) -5z(y-5z) = 4y²-25z²-5yz+25z²= 4y²-5yz
b) (3a+b)² - 2a (4a-b)=9a²+6ab+b²-8a²+2ab=a²+6ab+b²
c) (2a+3b)²-4a(a-2b)+(a+b)(a-9b)=4a²+12ab+9b²-4a²+8ab+a²-9b²=a²+20ab
d) (5y-2z)(5y+2z)+4z(y+z)-25y²=25y²-4z²+4yz+4z²=29y²+4yz
e) (x-1)²+17-(x+2)²+5(x-2)=x²-2x+1+17-x²-4x-4+5x-10=-x+4
f) 6x(x-3)+(2x+3)²-10x(x+1)+16x=6x²-18x+4x²+12x+9-10x²-10x+16x=9
g) 5a(3a-b)-(2a-b)²+4b(a-2b)+3b(3b-a)= 15a²-5ab-4a²+4ab+b²+4ab-8b²+9b²-3ab=11a²+6ab+2b²