Question

el tercer término de (4x - 3/2)6

Answer 1

Respuesta:

          $8640x^{4}$

Explicación paso a paso:

$(4x-\frac{3}{2} )^{6}$

$n = 6$

$a = 4x$

$b = -\frac{3}{2}$

$k = 3$

Fórmula:

$T_{k} = (\left \ {{n} \atop {k-1}} ) a^{n-k+1} b^{k-1}$

$T_{3} =(\left \ {{6} \atop {3-1}} ) (4x)^{6-3+1} (-\frac{3}{2}) ^{3-1}$

$T_{3} = (\left \ {{6} \atop {2}} ) (4x)^{4} (-\frac{3}{2} )^{2}$

$T_{3} = \frac{6!}{2!(6-2)!} (256x^{4} )(\frac{9}{4} ) = \frac{6!}{2!*4!} (\frac{2304x^{4} }{4} ) =\frac{6*5*4!}{2*1*4!} ( 576x^{4} ) = \frac{30}{2} * ( 576x^{4} )$

$T_{3} = 8640x^{4}$