Question

Doprowadź do najprostszej postaci:
a) 4(x-y)(3x+2y)+5y(x+y)=25y^2
b) 6 b(2a-b)+2(3a+2b)(3a-3b)-18a^2
c) (a+pierwiastek5)(a^2-5)(a-pierwiastek5)
d)2(3x^2-1)-(2x-1)(x+2)
e) 6a^2+5a(-a+2)-(4a-3)

Answer 1

4(x-y)(3x+2y)+5y(x+y)-25y^2=4(3X²+2xy-3xy-2y²)+5xy+5y²-25y²=12x²+8xy-12xy-8y²+5y²+5xy-25y²=12x²+1xy-28y²
b)6 b(2a-b)+2(3a+2b)(3a-3b)-18a^2=12ab-6b²+(6a+4b)(3a-3b)=12ab-6b²+18a² -18ab+12ab-12b²=-18b²+6ab+18a²
c)(a+√5)(a²-5)(a-√5)=(a²-√5²)(a²-5)=(a²-5)(a²-5)=(a²-5)²=a^4-10a²+25

d)2(3x^2-1)-(2x-1)(x+2)= 6x²-2-(2x²+4x-1x-2)=6x²-2-2x²-4x+1x+2=4x²-3x

e) 6a^2+5a(-a+2)-(4a-3)=6a²+(-5a²+10a)-4a+3=6a²-5a²+10a-4a+3=1a²+6a+3