Question

Determine o termo x^4 do desenvolvimento de (2x−3)^7​

Answer 1

Explicação passo-a-passo:

Termo geral do Binomio de newton :

Determinar o termo x⁴ no binômio (2x - 3)^7

$\mathsf{T_{p+1}~=~C^p_{n}.a^{n-p}.b^p }$

$\mathsf{T_{p+1}~=~C^p_{7}.(2x)^{7-p}.(-3)^p }$

$\mathsf{T_{p+1}~=~C^p_{7}.2^{7-p}.x^{7-p}.(-3)^p }$

Em particular :

7-p = 4

7 - 4 = p

p = 3

$\mathsf{T_{3+1}~=~C^3_{7}.2^{7-3}.x^{7-3}.(-3)^3 }$

$\mathsf{T_{4}~=~\dfrac{7!}{3!(7-3)!} .2^4.x^4.(-27) }$

$\mathsf{T_{4}~=~\dfrac{7!}{3!4!} . 16x^4.(-27) }$

$\mathsf{T_{4}~=~\dfrac{7.\cancel{6}.5.\cancel{4!}}{\cancel{6}.\cancel{4!}} . (-432x^4) }$

$\mathsf{T_{4}~=~35.(-432x^4) }$

$\boxed{\mathsf{T_{4}~=~-15120x^4 }}}}$

Espero ter ajudado bastante!)