Question

麻烦的数学计算题，求解答！！

[（a-b)^4+3(b-a)^3+2(b-a)^2]/[1/2(a-b)]^2

Answer 1

[（a-b)^4+3(b-a)^3+2(b-a)^2]/[1/2(a-b)]^2
=[(a-b)^4-3(a-b)^3+2(a-b)^2]/[1/4(a-b)^2]
=4[(a-b)^4-3(a-b)^3+2(a-b)^2]/(a-b)^2
=4(a-b)^2[(a-b)^2-3(a-b)+2]/(a-b)^2
=4[(a-b)^2-3(a-b)+2]
=4(a-b-2)(a-b-1)

Answer 2

原式=[(a－b)^4－3(a－b)^3＋2(a－b)²]/[(1/4)(a－b)²]
=4(a－b)²－12(a－b)＋8
=4(a²－2ab＋b²)－12a＋12b＋8
=4a²－8ab＋4b²－12a＋12b＋8

Answer 3

[（a-b)^4+3(b-a)^3+2(b-a)^2]/[1/2(a-b)]^2
=[（a-b)^4-3(a-b)^3+2(a-b)^2]*4 [(a-b)]^-2
=[（a-b)^2-3(a-b)+2]*4
=4*(a-b-1) *(a-b-2)

Answer 4

原式=4(a-b)^2-12(a-b)+8=(4a-4b-8)(a-b-1)

Answer 5

设b-a=t,
原式=(t^4+3t^3+2t^2)/(1/2t)^2
=t^2(t^2+3t+2)4t^2
=4t^4(t+1)(t+2)