Question

先化简,再求值:(a-b)(a+b)^2-(a+b)(a-b)^2+2b(a^2+b^2),其中a=1/2,b=-1

Answer 1

(a-b)(a+b)²-(a+b)(a-b)²+2b(a²+b²)
=(a+b)(a-b)[(a+b)-(a-b)]+2b(a²+b²)
=2b(a²-b²)+2b(a²+b²)
=2b(a²-b²+a²+b²)
=4a²b
=4×(1/2)²×(-1)
=-1

Answer 2

(a-b)(a+b)^2-(a+b)(a-b)^2+2b(a^2+b^2)
= (a-b)(a+b)[(a+b)-(a-b)] +2b(a^2+b^2)
= (a²-b²)*2b +2b(a²+b²)
= 2a²b
代入得：-1/2