Explicație pas cu pas:
termenul general al dezvoltării:
[tex]T_{k+1} = C_{n}^{k}\cdot a^{n-k}\cdot b^{k}[/tex]
=>
[tex]T_{k+1} = C_{12}^{k}\cdot \left(x^{ \frac{3}{4} } \right)^{12-k}\cdot 2^{k}[/tex]=>
[tex]\left(x^{ \frac{3}{4} } \right)^{12-k} = {x}^{6} < = > x^{ \frac{3(12 - k)}{4}} = {x}^{6} \\ = > \frac{3(12 - k)}{4} = 6 < = > 12 - k = 8 \\ = > k = 4[/tex]
=>
[tex]T_{4+1} = C_{12}^{4}\cdot \left(x^{6} \right)\cdot 2^{4} = > T_{5} = 7920 \cdot {x}^{6} \\ [/tex]
