Chứng minh các hằng đẳng thức sau :
a, \(\left(a^2-b^2\right)+\left(2ab\right)^2=\left(a^2+b^2\right)^2\)
b, \(\left(a^2+b^2\right).\left(c^2+d^2\right)=\left(ac+bd\right)^2+\left(ad-bc\right)^2\)
c, \(\left(ax+b\right)^2+\left(a-bx\right)^2+c^2x^2=\left(a^2+b^2+c^2\right).\left(x^2+1\right)\)
d, \(\dfrac{1}{2}.\left(a+b+c\right).\left[\left(a-b\right)^2+\left(b-c\right)^2+\left(c-a\right)^2\right]=a^3+b^3+c^3-3abc\)
e, \(1000^2+1003^2+1005^2+1006^2=1001^2+1002^2+1004^2+1007^2\)