More math questions?

Question

if you have like, (2x^2y^3)^3 would you get 8x^6y^9? and for (2x-9)^2, would you get 4x^2-81? if you have -3xy^3(x-2y) how would you do that? I know I learned it, but I kinda forgot... Please help!

Answer 1

(2x^2y^3)^3  =  (8x^6)(y^9)

(2x-9)^2 = 4x^2  - 36x  - 81; multiply this out term by term to see this.

-3xy^3(x-2y)  = -3(x^2)(y^3)  + 6xy^4

Answer 2

The first one is correct.  The second one (2x-9)^2 means (2x-9)(2x-9) so you have to "foil" it 4x^2-18x-18x+81 = 4x^2-36x+81.  The third one is just distribution, multiply the -3xy^3 to each of the terms inside (when multiplying, add exponents and don't forget that if the variable has no exponent then it is an invisible 1) So this one would be-3x^2y^3+6xy^4

Answer 3

(2x²y^3)^3=2^3(x²)^3(y^3)^3=8x^6y^9

(2x-9)²=4x²-36x+81

-3xy^3(x-2y)=-3x²y^3+6xy^4