How do you expand #(2x+3y)^4#?
1 Answer
Aug 28, 2017
Explanation:
#"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)!)#
#"we can also generate the binomial coefficients using"#
#"the appropriate row of "color(blue)"Pascal's triangle"#
#"for "n=4to1color(white)(x)4color(white)(x)6color(white)(x)4color(white)(x)1#
#"here "a=2x" and "b=3y#
#rArr(2x+3y)^4#
#=1.(2x)^4(3y)^0+4.(2x)^3(3y)^1+6.(2x)^2(3y)^2+4.(2x)^1(3y)^3+1.(2x)^0(3y)^4#
#=16x^4+96x^3y+216x^2y^2+216xy^3+81y^4#
