Expand (X-Y6) and (X-2Y4)

Question

Have to Binomal

Answer 1

Do you mean (X-Y)⁶ and (X-2Y)⁴? If so:

(1) (X-Y)⁶=

X⁶-6X⁵Y+(6)(5)X⁴Y²/2!-(6)(5)(4)X³Y³/3!+(6)(5)(4)(3)X²Y⁴/4!-(6)(5)(4)(3)(2)XY⁵/5!+Y⁶,

=X⁶-6X⁵Y+15X⁴Y²-20X³Y³+15X²Y⁴-6XY⁵+Y⁶. (Note the coefficients: 1 -6 15 -20 15 -6 1 are palindromic.)

(2) (X-2Y)⁴=

X⁴-4X³(2Y)+6X²(2Y)²-4X(2Y)³+(2Y)⁴,

=X⁴-8X³Y+24X²Y²-32XY³+16Y⁴.