Question

How do you find the 4th term in the expansion of the binomial `(x-10z)^7`?

Answer 1

`-35000x^4z^3`

Explanation:

`"using the "color(blue)"binomial theorem"`

`•color(white)(x)(x+y)^n=sum_(r=0)^n((n),(r))x^(n-r)y^r`

`"where " ((n),(r))=(n!)/(r!(n-r)!`

`"the general term is " ((n),(r))x^(n-r)y^r`

`"and " T_(r+1)=((n),(r))x^(n-r)y^rlarrcolor(red)" the nth term"`

`"here " x=x" and " y=-10z`

`color(blue)"for fourth term use r = 3"`

`rArrT_4=((7),(3))x^4(-10z)^3`

`color(white)(rArrT_4)=35x^4(-1000z^3)`

`color(white)(rArrT_4)=-35000x^4z^3`