1.[（3a+b）（3a-b）]^2
=[(3a)^2 - b^2]^2
=(9a^2 - b^2)^2
=81a^4 - 18a^2b^2 + b^4
2.（2x+y)^2（2x-y)^2
=[(2x+y)(2x-y)]^2
=[(2x)^2 - y^2]^2
=(4x^2 - y^2)^2
=16x^4 - 8x^2y^2 + y^4
3.（5m+2n)^2 —（5m-2n)^2
=[(5m+2n)+(5m-2n)][(5m+2n)-(5m-2n)]
=(10m)(4n)
=40mn
4.（-5x+3y-2z)^2
=25x^2 - 15xy + 10xz - 15xy + 9y^2 - 6yz + 10xz - 6yz + 4z^2
=25x^2 - 30xy + 20xz + 9y^2 - 12yz + 4z^2
5.（-a-b+3)^2
=a^2 + ab - 3a + ab + b^2 - 3b - 3a - 3b + 9
=a^2 + 2ab - 6a + b^2 - 6b + 9
6.（-3x-5y）²
=9x^2 + 30xy + 25y^2
7.（-2a+3b-5c）（-2a-3b+5c）
=[-2a+(3b-5c)][-2a-(3b-5c)]
=(-2a)^2 - (3b-5c)^2
=4a^2 - 9b^2 + 30bc - 25c^2
8.（3m-4n+2）（-3m-4n-2）
=-(3m-4n+2)(3m+4n+2)
=-[(3m+2)-4n][(3m+2)+4n]
=-[(3m+2)^2 - (4n)^2]
=-9m^2 - 12m - 4 + 16n^2
9.[x+(1/x)]^2 = x^2 + 2 + (1/x)^2 = 25
x^2 + 1/x^2 = 25-2=23
10.a^2 + b^2 = (a-b)^2 - 2ab = 7^2 - 2×2=49-4=45
11.x^2-8x+y^2+6y+25=0
(x^2-8x+16)+(y^2+6y+9)=0
(x-4)^2 + (y+3)^2=0
∵(x-4)^2和(y+3)^2恒≥0
∴x-4=0 ,y+3=0
x=4 ,y=-3