А) 1)(ab+b²)²=a²b²+2ab³+b^4
2)(a-b)²=a²-2ab+b²
3)(a²-ab)²=a^4-2a³b+a²b²
4) a²b²+2ab³+b^4 b²(a²+2ab+b²)
-------------------- = -------------------- = a²+2ab+b²
b² b²
5) a^4-2a³b+a²b² a²(a²-2ab+b²)
-------------------- = -------------------- = a²-2ab+b²
a² a²
6) a²+2ab+b²+a²-2ab+b²-(a²-2ab+b²) = 2a²+2b²-a²+2ab-b² = a²+2ab+b² = (a+b)²
При a=-2; b=-3,5 (a+b)²=(-2-3,5)²=(-5,5)²=30,25
б) ( a-1 a+1 ) ( 1 a 1 ) ( (a-1)² - (a+1)² ) * (2a-a²-1)
(------- - --------) * (----- - ----- - ----- ) = -------------------------------------- =
( a+1) a-1 ) ( 2 4 4a ) (a²-1) * 4a
(a²-2a+1-a²-2a-1)(-a²+2a-1) -4a(-a²+2a-1) 4a(a²-2a+1) (a-1)² a-1
-------------------------------------- = ------------------ = ----------------- = -------------- = --------
4a(a²-1) 4a(a²-1) 4a(a²-1) (a-1)(a+1) a+1
При a=-3,75 :
-3,75-1 -4,75 19 8
----------- = -------- = ---- = 1 ----
-3,75+1 -2,75 11 11