Question #14373

1 Answer
Nov 26, 2017

#81a^4-216a^3b+216a^2b^2-96ab^3+16b^4#

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)!)#

#"here "x=3a,y=-2b" and "n=4#

#rArr(3a-2b)^4#

#=((4),(0))(3a)^4(-2b)^0+((4),(1))(3a)^3(-2b)^1+((4),(2))(3a)^2(-2b)^2+((4),(3))(3a)^1(-2b)^3+((4),(4))(3a)^0(-2b)^4#

#"we can obtain the binomial coefficients using the"#
#"appropriate row of Pascal's triangle"#

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

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

#=1.81a^4-4.54a^3b+6.36a^2b^2-4.24ab^3+1.16b^4#

#=81a^4-216a^3b+216a^2b^2-96ab^3+16b^4#