How do you use the binomial theorem to expand and simplify the expression #(5-3y)^3#?

1 Answer
Oct 29, 2017

Answer:

#125-225y+135y^2-27y^3#

Explanation:

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

#•color(white)(x)(a+b)^n=sum_(r=0)^n""^nC_r a^(n-r)b^r#

#"where the binomial coefficient "#

#""^nC_r=(n!)/(r!(n-r)!)#

#"we can obtain the coefficients using the appropriate row"#
#"of "color(blue)"Pascal's triangle ""for n = 3"#

#rArrcolor(red)(1)color(white)(x)color(red)(3)color(white)(x)color(red)(3)color(white)(x)color(red)(1)#

#"here "a=5" and "b=-3y#

#rArr(5-3y)^3#

#=color(red)(1).5^3(-3y)^0+color(red)(3).5^2(-3y)^1+color(red)(3).5^1(-3y)^2+color(red)(1).5^0(-3y)^3#

#=125-225y+135y^2-27y^3#