Question

1. (x+7)² ; (3x-2)² ; (x-6)(x+6)
2. Descompuneti: x²+12x+36 ; 25x²-10xy+y2 ; 81x²-49y² ; x^4+4
3.Grupati favorabil: a²x+b²-a²y-b²y ; x³+4x²+4x+16
4. Rezolvati ecuatiile: x²=36 ; (x+2)²=12
Daca ar putea cineva sa imi dea exact toate formulele de calcul prescurtat pentru ca maine am test si am nevoie :)

Answer 1

(x+7)²=x²+14x+49
(3x-2)²=9x²-12x+4
(x+6)(x-6)=x²-36

x²+12x+36=x²+2·x·6+6²=(x+6)²
25x²-10xy+y²=(5x)²-2·5x·y+y²=(5x-y)²
81x²-49y²=(9x+7y)(9x-7y)

a²x+b²-a²y-b²y=a²(x-y)+b²(1-y)
x³+4x²+4x+16=x²(x+4)+4(x+4)=(x²+4)(x+4)

x²=36
x=√36
x=6 sau -6
(x+2)²=12
x+2=√12
x+2=2√3 sau -2√3
x=2√3-2 sau -2√3-2
x=2(√3-1) sau x=-2(√3+1)

Answer 2

1. (x+7)² =x²+14x+49
 (3x-2)²=9x²-12x+4
 (x-6)(x+6)=x²-36
2. Descompuneti:
 x²+12x+36 =(x+6)²
 25x²-10xy+y²=(5x-y)²
 81x²-49y² =(9x-7y)(9x+7y)
 x⁴+4 =(x²+2-2x)(x²+2+2x)
3.Grupati favorabil:
a²x+b²-a²y-b²y =a²x-a²y+b²-b²y =a²(x-y)-y(a²+b²)
 x³+4x²+4x+16=x²(x+4)+4(x+4)=(x+4)(x²+1)
4. Rezolvati ecuatiile:
 x²=36       x₁=6   x₂=-6
 (x+2)²=12
solutia 1
x+2=2√3
x=2√3-2

solutia 2
x+2=-2√3
x=-2√3-2