Answer to Question #32186 in Algebra for yashas

Question

expand[3a-2b]^3

Answer 1

In this taks we'll binom formula. We know formula for the third power of binom ( x - y )^3= x^3 -3x^2 * y + 3x*y^2 - y^3
In our case x=3a, y=2b, so we obtain
[3a-2b]^3 = ( 3a )^3 - 3*(3a)^2 * (2b) + 3*(3a)*(2b)^2 - ( 2b)^3= 27a^3 -3*9*a^2 * 2* b + 3*3*a*4*b^2 - 8*b^3=
=27a^3 -54*a^2 * b + 36*a*b^2 - 8*b^3