Zad 1 Wykonaj dzialania :
a) 3(5x-2) - (2x-1)(3x+1) = ?
b) (2b-5)(3-2b) - (3b+2)(b-6) = ?
Zad 2 Zapisz w jak naprostszej postaci :
a) (2a-1)(2a+1) - (a+1)² =
b) x(2x-1)² - 2x(x-1)(x+1) =
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1) (15x-6)-(6x+2x-3x-1)=15x-6-6x-2x+3x+1=10x-5
(6b-4b-15+10b)-(3b2-18b+2b-12)=12b-15-3b2+18b-2b+12=-3b2+28b-3
2) (4a2+2a-2a-1)-(a2+2a+1)=4a2-1-a2-2a-1=2a2-2a-1
x(4x2+4x+2)-2x(x2+x-x-1)=4x3+4x2+2x-4x3+2x)=4x2+4x=4x(x+1)
np. 4x2 --> to jest kwadrat :)
zad.1.
a) 3(5x-2) - (2x-1)(3x+1) =15x-6-6x^2-2x+3x+1=-6x^2+16x-5
b) (2b-5)(3-2b) - (3b+2)(b-6) =6b-4b^2-15+10b-(3b^2-18b+2b-12)=6b-4b^2-15+10b-3b^2+18b-2b+12=-7b^2+32b-3
zad.2.
a) (2a-1)(2a+1) - (a+1)² =4a^2+2a-2a-1-a^2-2a-1=3a^2-2a-2
b) x(2x-1)² - 2x(x-1)(x+1) =x(4x^2-4x+1)-2x(x^2-1^2)=4x^3-4x^2+x-2x^3+2x=2x^3-4x^2+3x