Question

Calculati,utilizand formulele de calcul prescurtat:

a)(x+3)²+(x-1)²-2x²
b)(2x+7)²-(3x+5)²+(2x+5)
c)(x-4)²-(x-3)·(x+3)+2(x+1)²
d)(2x-3)²-4(x-6)·(x+6)+(x-9)(x+9)+x²
e)(5x-1)(5x+1)-(4x+3)²+2(3x-1)²
f)(3+2x)²-(x+2)·(x-2)+4(x-3)²
g)(6x-1)²-9(x-1)(x+1)+3(2x-7)2

Answer 1

a)(x+3)²+(x-1)²-2x²=
(x²+6x+9)+(x²-2x+1)-2x²=
x²+6x+9+x²-2x+1-2x²=
4x+10⇒x=-10/4

b)(2x+7)²-(3x+5)²+(2x+5)=
(4x²+28x+49)-(9x²+30x+25)+(2x+5)=
4x²+28x+49-9x²-30x-25+2x+5=
-5x²-29

c)(x-4)²-(x-3)(x+3)+2(x+1)²=
(x²-8x+16)-(x²-9)+2(x²+2x+1)=
x²-8x+16-x²+9+2x²+4x+2=
2x²-4x+27

d)(2x-3)²-4(x-6)(x+6)+(x-9)(x+9)+x²=
(4x²-12x+9)-4(x²-36)+(x²-81)+x²=
4x²-12x+9-4x²+36+x²-81+x²=
2x²-12x-36

e)(5x-1)(5x+1)-(4x+3)²+2(3x-1)²=
25x²-1-(16x²+24x+9)+2(9x²-6x+1)=.
25x²-1-16x²-24x-9+18x²-12x+2=
27x²-36x-8

f)(3+2x)²-(x-2)(x+2)+4(x-3)²=
(9+12x+4x²)-(x²+4)+4(x²-6x+9)=
4x²+12x+9-x²-4+4x²-24x+36=
7x²-12x+41

g)(6x-1)²-9(x-1)(x+1)+3(2x-7)²=
(36x²-12x+1)-9(x²-1)+3(4x²-28x+49)=
36x²-12x+1-9x²+9+12x²-84x+147=
39x²-96x+63