解答
展开 (y2x4−xy2)10
解答
y101024x40−y75120x35+y411520x30−y15360x25+13440x20y2−8064x15y5+3360x10y8−960x5y11+180y14−x520y17+x10y20
求解步骤
(y2x4−xy2)10
使用二项式定理: (a+b)n=i=0∑n(in)a(n−i)bia=y2x4,b=−xy2
=i=0∑10(i10)(y2x4)(10−i)(−xy2)i
展开求和
=0!(10−0)!10!(y2x4)10(−xy2)0+1!(10−1)!10!(y2x4)9(−xy2)1+2!(10−2)!10!(y2x4)8(−xy2)2+3!(10−3)!10!(y2x4)7(−xy2)3+4!(10−4)!10!(y2x4)6(−xy2)4+5!(10−5)!10!(y2x4)5(−xy2)5+6!(10−6)!10!(y2x4)4(−xy2)6+7!(10−7)!10!(y2x4)3(−xy2)7+8!(10−8)!10!(y2x4)2(−xy2)8+9!(10−9)!10!(y2x4)1(−xy2)9+10!(10−10)!10!(y2x4)0(−xy2)10
化简 0!(10−0)!10!(y2x4)10(−xy2)0:y101024x40
化简 1!(10−1)!10!(y2x4)9(−xy2)1:−y75120x35
化简 2!(10−2)!10!(y2x4)8(−xy2)2:y411520x30
化简 3!(10−3)!10!(y2x4)7(−xy2)3:−y15360x25
化简 4!(10−4)!10!(y2x4)6(−xy2)4:13440x20y2
化简 5!(10−5)!10!(y2x4)5(−xy2)5:−8064x15y5
化简 6!(10−6)!10!(y2x4)4(−xy2)6:3360x10y8
化简 7!(10−7)!10!(y2x4)3(−xy2)7:−960x5y11
化简 8!(10−8)!10!(y2x4)2(−xy2)8:180y14
化简 9!(10−9)!10!(y2x4)1(−xy2)9:−x520y17
化简 10!(10−10)!10!(y2x4)0(−xy2)10:x10y20
=y101024x40−y75120x35+y411520x30−y15360x25+13440x20y2−8064x15y5+3360x10y8−960x5y11+180y14−x520y17+x10y20