a: \(=x^2+2xy+y^2+x^2-2xy+y^2\)
\(=2x^2+2y^2\)
b: \(\left(2a+b\right)^2-\left(b-2a\right)^2\)
\(=\left(2a+b+b-2a\right)\left(2a+b-b+2a\right)\)
\(=4a\cdot2b=8ab\)
c: \(\left(6x+\dfrac{1}{2}\right)\left(36x^2-3x+\dfrac{1}{4}\right)\)
\(=\left(6x+\dfrac{1}{2}\right)\cdot\left[\left(6x\right)^2-6x\cdot\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2\right]\)
\(=216x^3+\dfrac{1}{8}\)
d: \(\left(x-5y^2\right)\left(x^2+5xy^2+25y^4\right)\)
\(=x^3-125y^6\)