怎样计算：（x-1)（x-2）（x-3）(x-4） 有啥简便方法？ x+1 x+2 x+3 x+4

• （x-1)(x-2)(x-3)(x-4)怎么算，要用简便的方法来算
• (X-1)(X-2)(X-3)(X-4)=?简便方法
• （x-1)(x-2)(x-3)(x-4)-120 谁能告诉我过程的答案，化简的，
• y=(x-1)(x-2)^2(x-3)^3(x-4)^4求导

（x-1)(x-2)(x-3)(x-4)怎么算，要用简便的方法来算

（x-1)(x-2)(x-3)(x-4)

=[(x-1)(x-4)][(x-2)(x-3)]

=(x^2-5x+4)(x^2-5x+6)

=(x^2-5x)^2+10(x^2-5x)+24

=x^4-10x^3+25x^2+10x^2-50x+24

=x^4-10x^3+35x^2-50x+24

(X-1)(X-2)(X-3)(X-4)=?简便方法

(X-1)(X-2)(X-3)(X-4)

= [(x  -1)(x-4)] * [(x-2)(x-3)]

= [x^2 - 5x  +4] * [[x^2 - 5x + 6]

= (x^2 - 5x)^2 + (4 + 6)* (x^2 - 5x) + 4 * 6

= (x^2 - 5x)^2 + 10(x^2 - 5x) + 24

= x^2 - 10x^3 + 25x^2 + 10x^2 - 50x + 24

= x^4 - 10x^3 + 35x^2 - 50x + 24

（x-1)(x-2)(x-3)(x-4)-120 谁能告诉我过程的答案，化简的，

（x-1)(x-2)(x-3)(x-4)-120

=[(X-1)(X-4)][(X-2)(X-3)]-120

=[(X²-5X)+4][(X²-5X)+6]-120

=(X²-5X)²+10(X²-5X)+24-120

=(X²-5X)²+10(X²-5X)-96

=(X²-5X-6)(X²-5X+16)

=(X-6)(X+1)(X²-5X+16)

y=(x-1)(x-2)^2(x-3)^3(x-4)^4求导

lny=ln(x-1)+2ln(x-2)+3ln(x-3)+4ln(x-4)

y'/y=1/(x-1)+ 2/(x-2) +3/(x-3) +4/(x-4)

∴y'=(x-2)²(x-3)^3(x-4)^4 +2(x-1)(x-2)(x-3)^3(x-4)^4 +3(x-1)(x-2)^2(x-3)^2(x-4)^4

+4(x-1)(x-2)²(x-3)³(x-4)³