How do you expand #(x-3y)^4#?

1 Answer
Jul 26, 2017

Answer:

#x^4-12x^3y+54x^2y^2-108xy^3+81y^4#

Explanation:

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

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

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

#"the coefficients can be generated using the appropriate"#
#"row of "color(blue)"Pascal's triangle"#

#"for n =4 the row of coefficients is"#

#1color(white)(x)4color(white)(x)6color(white)(x)4color(white)(x)1#

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

#rArr(x-3y)^4#

#=1.x^4(-3y)^0+4.x^3(-3y)^1+6.x^2(-3y)^2+4.x^1(-3y)^3+1.x^0(-3y)^4#

#=x^4-12x^3y+54x^2y^2-108xy^3+81y^4#