Question

Calculati, folosind formulele de calcul prescurtat:
a)   (x+2)(x-2)+(x+4)²-2x=?
b)   (2-x)²-(x+3)(x-3)-x(x-1)=?
c)   (x+5)²-2(x-5)(x+5)+x²=?
d)   (6-x)²-3(x+2)-5(x+1)=?
As vrea rezolvarile complete, varog.

Answer 1

a) x²-4+x²+8x+16-2x=2x²-10x+12=2(x²-5x+6)=2(x-2)(x-3)
b) 4-4x+x²-x²+9-x²+x=-x²-3x+13
c) (x+5)²-2(x-5)(x+5)+x²-10x+25+10x-25=(x+5)²-2(x-5)(x+5)+(x-5)²+10x-25=(x+5-x+5)²+10x-25=10+10x-25=10x-15=5(2x-3)
d) 36-12x+x²-3x-6-5x-5=x²-20x+25

Answer 2

x^2-4+x^2+8x+16-2x=2x^2+6x+12=2(x^2+3x+6)
4 - 4x + x^2 - x^2 + 9 - x^2 + x =13 - 3x - x^2
x^2 + 10x +25 - 2(x^2 - 25) + x^2 = x^2 + 10x +25 - 2x^2 + 50 + x^2 = 10x+75
36 - 12x + x^2 - 3x - 6 - 5x - 5 = x^2 - 20x +25