1) а²+в²+ав а²в² а²+в² ав²
...= -------------- *---------- * ---------------------- =---------
а а²+в² (а-в)(а²+ав+в²) а-в
2) М=а-3, N=a²-8a+6, P=a-8, Q=a²-3a+5
MN-PQ=a³-8a²+6a-3a²+24a-18-(a³-3a²+5a-8a²+24a-40)=a+22
4)a⁵+a⁴-2a³-2a²+a+1= a⁴(a+1)-2a²(a+1)+(a+1)=(a+1)(a⁴-2a²+1)=(a+1)(a²-1)²
5) 3²-1 4²-1 5²-1 101²-1 (3-1)(3+1)(4-1)(4+1)*...*(101-1)(101+1)
.... =------ * -------* ------* ... * ------------- = ----------------------------------------------------- =
3² 4² 5² 101² 3²*4²*...*101²
(2*4)*(3*5)*(4*6)*(5*7)*...*(100*102) 2*(3*4*5*6*...101)² * 102
=---------------------------------------------------- =----------------------------------- = 2*102=204
(3*4*5*6*...*101)² (3*4*5*6*...*101)²