Упростить выражение 1) (2x-y) (4x^2 + 2xy +y^2) (8x^3+y^3) 2) (x-2)^3-(x+2)^3 3)...

Question

Упростить выражение
1) (2x-y) (4x^2 + 2xy +y^2) (8x^3+y^3)
2) (x-2)^3-(x+2)^3
3) (a^6-3a^3+9) (a^3+3)-a^9
4) (a+3)^3-(a-1)^3-12a^2

Answer 1

1) (2x-y) (4x^2 + 2xy +y^2) (8x^3+y^3)=(8x³-y³)(8x³+y³)=64x^6-y^6
2) (x-2)^3-(x+2)^3=(x-2-x-2)((x²-4x+4+x²-4+x²+4x+4)=-4(3x²+4)
3) (a^6-3a^3+9) (a^3+3)-a^9=a^9 +27-a^9=27
4) (a+3)^3-(a-1)^3-12a^2 =(a+3-a+1)(a²+6a+9+a²+2a-3+a²-2a+1)-12a²=
=4(3a²+6a+7)-12a²=12a²+24a+28-12a²=24a+258=4(6a+7)

Answer 2

1) (2x-y) (4x² + 2xy +y²) (8x³+y³)=(8x³-y³)(8x³+y³)=64x⁶-y⁶
2) (x-2)³ - (x+2)³ = x³-6x²+12x-8-x³-6x²-12x-8=-12x²-16
3) (a⁶-3a³+9)(a³+3)-a⁹ = a⁹+27-a⁹=27
4) (a+3)³-(a-1)³-12a²=a³+9a²+27a+27-a³+3a²-3a+1-12a²=24a+28