Question

(а^3-9)(а^6+9а^3+81)-а^9-729=...

Answer 1

(а^3-9)(а^6+9а^3+81)-а^9-729= a^9+ a^6⋅9+ a^3⋅81−9 a^6−81 a^3−729− a^9−729=9 a^6−9 a^6−1458=−1458

Answer 2

We can simplify the expression using the difference of squares formula:

(a^3-9)(a^6+9a^3+81) - a^9 - 729 = [(a^3)^2 - 3^2][(a^3)^2 + 3(a^3) + 3^2] - (a^3)^3 - 3^6 (using a^3 = x substitution) = (a^3 - 3)(a^6 + 3a^3 + 9)(a^3 + 3)(a^6 - 3a^3 + 9) - a^9 - 729 = [(a^3 - 3)(a^6 + 3a^3 + 9)(a^3 + 3)(a^3 - 3)(a^3^2 + 3a^3 + 9)] - (9a^3)^2 - 729 = (a^3 - 3)^2(a^3 + 3)^2(a^3^2 + 3a^3 + 9) - 9^2a^6 - 729 = (a^6 - 6a^3 + 9)(a^6 + 6a^3 + 9)(a^3^2 + 3a^3 + 9) - 81a^6 - 729 = (a^6)^2 + 9(a^6) + 27(a^6) + 27(a^3)^3 - 54(a^6) - 54(a^3)^3 + (81)^2 - 81(a^6) - 729 = a^12 - 27a^9 + 243a^6 - 729

Therefore, (a^3-9)(a^6+9a^3+81) - a^9 - 729 simplifies to a^12 - 27a^9 + 243a^6 - 729.