Răspuns:
2025*1012+2025=2025*1013= 2051325
Explicație pas cu pas:
((1+x)+x^2))^2025= Comb de 2025 luate cate 0*(1+x) ^2025*(x²) ^0+
Comb de 2025 luate cate 1 *(1+x)^2024*(x²)^1 +
Comb de 2025 luatec cate2*(1+x)^2023*(x²)²+
...............................................................................................................+
Comb de 2025 luate cate 2025 (1+x)^0*(x²)^2025
termeni in x² avem doar de la
- primul termen , termenul in x² din (1+x)^2025 si x² ^0
adica (Cde 2025luate cate 2023*1^2023*x²) *x²^0= 2025*2024/2=1012*2025
- de la al doilea termen, Comb de 2025 luatev cate 1 (1+Comb de 2024 luate cate0*x+ Comb de 2024 luate cate2*x²+..) *x²^1..... adica 2025*1
total
2025*1012+2025=2025*1013= 2051325
