因式分解题。

(1)(a+b)^2－(a-b)^2
=[(a+b)+(a-b)][(a+b)-(a-b)]
=(a+b+a-b)(a+b-a+b)
=2a*2b
=4ab

(2)x^3+x^2y-xy^2-y^3
=x^2(x+y)-y^2(x+y)
=(x+y)(x^2-y^2)
=(x+y)^2(x-y)

(3)(5m^2+3n^2)^2－(3m^2+5n^2)^2
=[(5m^2+3n^2)+(3m^2+5n^2)][(5m^2+3n^2)-(3m^2+5n^2)]
=(8m^2+8n^2)(2m^2-2n^2)
=16(m^2+n^2)(m+n)(m-n)

2.将一条长100cm的金色彩带剪成两段，恰好可以装饰两张大小不等的正方形油画（不计接头重叠部分），若两张油画的面积相差50cm^2，问这两条彩带应剪多长？
设一根xcm，另一根100-xcm，不妨设x>100-x,x>50
这就是正方形的边长
则两个正方形边长是x/4,(100-x)/4
所以面积差=(x/4)^2-[(100-x)/4]^2
=[x/4+(100-x)/4][x/4-(100-x)/4]
=100*(x/2-100/4)=50
x/2-25=50/100=1/2
x=50+1=51
100-x=49
所以一根51cm，一根49cm

(1)(a+b+a-b)(a+b-a+b)=2a*2b=4ab
(2)x^2(x+y)-y^2(x+y)=(x+y)(x-y)(x+y)=(x-y)(x+y)^2
(3)(5m^2+3n^2+3m^2+5n^2)(5m^2+3n^2-3m^2-5n^2)=(8m^2+8n^2)(2m^2-2n^2)=16(m^2+n^2)(m^2-n^2)=16(m^2+n^2)(m+n)(m-n)