annabethschwartz annabethschwartz
  • 03-02-2020
  • Mathematics
contestada

Coefficient of x^4 in (2x-1)^5

Respuesta :

frika
frika frika
  • 10-02-2020

Answer:

[tex]-80[/tex]

Step-by-step explanation:

Use binomial expansion formula:

[tex](a+b)^n=a^n+C^n_1a^{n-1}b^1+C_2^na^{n-2}b^2+...+b^n[/tex]

In your case,

[tex](2x-1)^5=\\ \\=(2x)^5+C^5_1(2x)^4(-1)^1+C^5_2(2x)^3(-1)^2+C^5_3(2x)^2(-1)^3+C^5_4(2x)^1(-1)^4+(-1)^5[/tex]

Find the term containing [tex]x^4[/tex]:

[tex]C^5_1(2x)^4(-1)^1=\dfrac{5!}{1!(5-1)!}\cdot 16x^4\cdot (-1)=-5\cdot 16x^4=-80x^4[/tex]

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