Question

(x²-x-2)的6次方展开式？

Answer 1

（x^2-x-2)^6=[x^2-(x+2)]^6
=(x^2)^6-6(x^2)^5*(x+2)+15(x^2)^4*(x+2)^2-20(x^2)^3*(x+2)^3
+15(x^2)^2*(x+2)^4-6(x^2)*(x+2)^5+(x+2)^6
=x^12-6x^10*(x+2)+15x^8*(x^2+4x+4)-20x^6*(x^3+6x^2+12x+8)
+15x^4(x^4+8x^3+24x^2+32x+16)-6x^2*(x^5+10x^4+40x^3+80x^2+80x+32)
+x^6+12x^5+60x^4+160x^3+240x^2+192x+64
=x^12-6x^11-12x^10
...........................+15x^10+60x^9+60x^8
.............................................-20x^9-120x^8-240x^7-160x^6
...........................................................+15x^8+120x^7+360x^6+480x^5+240x^4
.................................................................................-6x^7-60x^6-240x^5-480x^4-480x^3
-192x^2
................................................................................................+x^6+12x^5+60x^4+160x^3
+240x^2+192x+64
=x^12-6x^11+3x^10+40x^9-45x^8-126x^7+141x^6+252x^5-180x^4-320x^3
+48x^2+192x+64.

Answer 2

x12次方一x6次方一2的6次方

Answer 3

(x²-x-2)的6次方展开式为：x¹² - 6x¹¹ + 21x¹⁰ - 56x⁹ + 126x⁸ - 210x⁷ + 252x⁶ - 210x⁵ + 126x⁴ - 56x³ + 21x² - 6x - 2。