Question

Ache o 5° termo do Binômio;
a) (4x - 3y) *6 b) (2x + y) *8

Answer 1

Termo geral:

$\boxed{T_{p+1} = \begin{pmatrix} n\\ p \end{pmatrix} \cdot a^{p} \cdot x^{n-p}}$

a) Para ser o 5° termo, o "T" tem que valer 5. E para isso:

p+1 = 5
p = 5-1
p = 4

Voltando:

$T_{4+1} = \begin{pmatrix} 6\\ 4 \end{pmatrix} \cdot (-3y)^{4} \cdot (4x)^{6-4} \\\\ T_{5} = \frac{6!}{(6-4)! \cdot 4!} \cdot (-3y)^{4} \cdot (4x)^{2} \\\\ T_{5} = \frac{6!}{2! \cdot 4!} \cdot 81y^{4} \cdot16x^{2} \\\\ T_{5} = 15 \cdot 81y^{4} \cdot 16x^{2} \\\\ \boxed{\boxed{T_{5} = 19440y^{4}x^{2}}}$


b)
$T_{4+1} = \begin{pmatrix} 8 \\ 4 \end{pmatrix} \cdot (y)^{4} \cdot (2x)^{8-4} \\\\ T_{5} = \frac{8!}{(8-4)! \cdot 4!} \cdot (y)^{4} \cdot (2x)^{4} \\\\ T_{5} = 70 \cdot y^{4} \cdot 16x^{4} \\\\ \boxed{\boxed{T_{5} = 1120y^{4}x^{4}}}$