Question

Por favor me ajudem.
Determine o termo em x^4, no desenvolvimento de ( 2x - 3/ x²)^6.

Answer 1

$T _{p+1} = \left(\begin{array}{ccc}n\\p\\\end{array}\right) (ax)^n^-^p . b^p \\ T _{p+1 } = \left(\begin{array}{ccc}7\\p\\\end{array}\right)(2x)^7^-^p . (3.x^-^2)^p \\ T _{p+1} = \left(\begin{array}{ccc}7\\p\\\end{array}\right)(2)^7-^p .x^7^-^p.3^p.x^-^2^p \\ T _{p+1} = \left(\begin{array}{ccc}7\\p\\\end{array}\right). 2^7^-^p . 3^p .x^7^-^3^p \\ Logo: 7 - 3p = 4 =\ \textgreater \ -3p = -3 =\ \textgreater \ p = 1 \\ T _{1+1} = \left-(\begin{array}{ccc}7\\1\\\end{array}\right) 2^6.3.x^4 = \frac{-7!}{6!1!}. 192.x^4=-1344x^4$