一、(1)(-1/3 m+5n)²=1/9m²-10/3mn+25n²
二、(1)(3a+2b)²
=(3a)²+2×3a×2b+(2b)²
=9a²+12ab+4b²
(2)(-x+2y)²
=x² -4xy+4y²
(3)(a+b)(-a-b)
=-(a+b)(a+b)
=-(a²+2ab+b²)
=-a²-2ab-b²
(4)(x+y)²-(x+y)(x-y)
=(x+y)(x+y-x+y)
=(x+y)2y
=2xy+2y²
三、(1)(2a+b)²-2a(a-b)-(2a²+b²)
=4a²+b²+4ab-2a²+2ab-2a²-b²
=6ab
∴当a=√3+1,b=√3-1时
原式=6(√3+1)(√3-1)=6×2=12
(2)(3x+2)(3x-2)-5x(x-1)-(2x-1)²
=9x²-4-5x²+5x-(4x²+1-4x)
=9x²-4-5x²+5x-4x²-1+4x
=9x-5
∴当x=-1/3时,
原式=9×(-1/3)-5=-8
(3)(a+b)²+(a-b)(2a+b) -3a²
=a²+2ab+b²+2a²-ab-b²-3a²
=ab
∴当a=-2-√3,b=√3-2时,
原式=(-2-√3)(√3-2)=-(2+√3)(√3-2)=-(3-4)=1