E(n)=(n²+n+1)²-(n²+n)²-n²
folosim formula (a+b)²=a²+2ab+b² ⇒(n²+n)²=[tex] n^{4} [/tex]+2n³+n²
a=n²
b=n
folosim formula (a+b+c)²=a²+b²+c²+2ab+2ac+2bc
(n²+n+1)²=[tex] n^{4} [/tex]+n²+1+2n³+2n²+2n
a=n²
b=n
c=1
E(n)=[tex] n^{4} [/tex]+n²+1+2n³+2n²+2n -[tex] n^{4} [/tex]-2n³-n²-n²=n²+2n+1=(n+1)² e patrat perfect (deoarece se scrie ca ceva la a doua!)
