1.a) 3a(a-2)+(a+1)(a+3)=[tex] 3a^{2} -6a +a^{2}+3a+a+3=4a^{2}-2a+3[/tex]
b)(3x-4)(3x+4) = [tex] 9x^{2} -16[/tex]
c)3+2√3+1=4+2√3
d)(√10-√7)(√10+√7)=10-7=3
2.a)4x^2+7=x(4x+7)
b)a^3-5a^2+a-5=a^2(a-5)+(a-5)=(a-5)(a^2+1)
c)x^2+12x+36=[tex] (x+6)^{2} =(x+6)(x+6)[/tex]
d)9x^2-12x+4=[tex] (3x-2)^{2} =(3x-2)(3x-2)[/tex]
e)16a^2-25b^2=(4a-5b)(4a+5b)
3.Consideram primul numar x, urmatoarele vor fi x+1, x+2,x+3,x+4.
Suma = x+x+1+x+2+x+3+x+4=5x+10=5(x+2) - care este multiplu de 5 deoarece 5(x+2) | 5 oricare ar fi x∈R
