6. formula a²+2ab+b²=(a+b)² sau a²-2ab+b²=(a-b)²
4a²+4ab+b²=(2a+b)²
a²-6ab+9b²=(a-3b)²
9a²+6ab+b²=(3a+b)²
9a²/16-2ab+16b²/9=(3a/4+4b/3)²
4x²/9+2xy+9y²/4=(2x/3+3y/2)² (aici in exercitiu era gresit 2ax trebuia 2xy)
4m²+12m+9=(2m+3)²
4+0,25x²-2x=4+x²/4-2x=(2+x/2)²
7. formula a²-b²=(a+b)(a-b)
4a²-1=(2a+1)(2a-1)
1-9a²=(1+3a)(1-3a)
25-16c²=(5+4c)(5-4c)
m²-a²=(m+a)(m-a)
-n²+b²=b²-n²=(b+n)(b-n)
a²-9y²=(a+3y)(a-3y)
81x²-y²=(9x+y)(9x-y)
36p²-c²=(6p+c)(6p-c)
49x²-121a²=(7x+11a)(7x-11a)
4x²/9-9/16=(2x/3-3/4)(2x/3+3/4)
x²y²-4a²/25=(xy-2a/5)(xy+2a/5)
a²c²-1/9=(ac-1/3)(ac+1/3)
8. formula a³-b³=(a-b)(a²+ab+b²) sau a³+b³=(a+b)(a²-ab+b²)
x³-1=(x-1)(x²+x+1)
a³+8=(a+2)(a²-2a+4)
64x³-27=(4x-3)(16x²+12x+9)
125a³+8b³=(5a+2b)(25a²-10ab+4b)
x³/27-8y³/27=(x/3-2y/3)(x²/9+2xy/6+4y²/9)
x³-125y⁹=(x-5y³)(x²+5xy³+25y⁶)
0,001x³+0,008y⁶=(0,1x+0,2y²)(0,01x²+0,02xy²+0,04y⁴)
64-a⁶b⁹=(4-a²b³)(16+4a²b³+a⁴b⁶)
12.
(x-3)²+2(x-3)(x+2)+(x+2)²=(x-3+x+2)²=(2x-1)²
x²+2xy+y²-z²-2zt-t²=(x+y)²-(z+t)²=(x+y+z+t)(x+y-z-t)
4x²-4xy+y²-z²=(2x-y)²-z²=(2x-y+z)(2x-y-z)
a⁴+b⁴-3a²b²=a⁴+b⁴-2a²b²-a²b²=(a²-b²)²-a²b²=(a²-b²+ab)(a²-b²-ab)
a⁴-2a³+2a²-2a+1=a⁴+2a²+1-2a³-2a=(a²+1)²+2a(a²+1)=(a²+1)(a²+1+2a)=
=(a²+1)(a+1)²
x⁴-2x³+2x-1=(x⁴-1)-2x(x²-1)=(x²-1)(x²+1)-2x(x²-1)=(x²-1)(x²+1-2x)=
=(x-1)(x+1)(x-1)²=(x+1)(x-1)³
