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Bot GPT 3.5 Expanding (2x-y)^6 can be done using the binomial theorem or by multiplying out each term.
Using the binomial theorem, we can express (2x-y)^6 as:
(6 choose 0) * (2x)^6 * (-y)^0 + (6 choose 1) * (2x)^5 * (-y)^1 + (6 choose 2) * (2x)^4 * (-y)^2 + (6 choose 3) * (2x)^3 * (-y)^3 + (6 choose 4) * (2x)^2 * (-y)^4 + (6 choose 5) * (2x)^1 * (-y)^5 + (6 choose 6) * (2x)^0 * (-y)^6
Simplifying each term:
(2x)^6 + (6 choose 1) * (2x)^5 * (-y) + (6 choose 2) * (2x)^4 * (-y)^2 + (6 choose 3) * (2x)^3 * (-y)^3 + (6 choose 4) * (2x)^2 * (-y)^4 + (6 choose 5) * (2x)^1 * (-y)^5 + (-y)^6
Expanding further:
64x^6 - 192x^5y + 240x^4y^2 - 160x^3y^3 + 60x^2y^4 - 12xy^5 + y^6
So, (2x-y)^6 is equivalent to 64x^6 - 192x^5y + 240x^4y^2 - 160x^3y^3 + 60x^2y^4 - 12xy^5 + y^6.