Respuesta :

Answer:

The coefficient of x³ = -160.

Step-by-step explanation:

We can find the coefficient of x³ in the expansion of (2x-5)⁴ by using the Binomial Formula:

[tex]\boxed{_nC_i\cdot x^{n-i}\cdot y^i}[/tex]

Given:

  • [tex]n=4[/tex] (highest degree of polynomial = 4)
  • [tex]n-i=3[/tex] (degree of x³ = 3)

        [tex]4-i=3[/tex]

              [tex]i=1[/tex]

  • [tex]x=2x[/tex]
  • [tex]y=-5[/tex]

The term of x³ [tex]=_4C_1\cdot (2x)^{4-1}\cdot (-5)^1[/tex]

                        [tex]=\displaystyle\frac{4!}{1!3!} (2x)^3(-5)[/tex]

                        [tex]=4(8x^3)(-5)[/tex]

                        [tex]=-160x^3[/tex]

Hence, the coefficient of x³ = -160.

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