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

1 Answer
Jul 7, 2017

Answer:

#-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#