a) \(\left(a^3-b^3\right)+\left(a-b\right)^2\)

\(=\left(a-b\right)\left(a^2+ab+b^2\right)+\left(a-b\right)^2\)

\(=\left(a-b\right)\left(a^2+ab+b^2+a-b\right)\)

b) \(\left(x^2+1\right)^2-4x^2\)

\(=\left(x^2+1\right)^2-\left(2x\right)^2\)

\(=\left(x^2+1-2x\right)\left(x^2+1+2x\right)\)

\(=\left(x-1\right)^2\left(x+1\right)^2\)

c) \(\left(y^3+8\right)+\left(y^2-4\right)\)

\(=\left(y^3+2^3\right)+\left(y^2-2^2\right)\)

\(=\left(y+2\right)\left(y^2-2y+4\right)+\left(y-2\right)\left(y+2\right)\)

\(=\left(y+2\right)\left(y^2+2y+4+y-2\right)\)

\(=\left(y+2\right)\left(y^2+3y+2\right)\)

d) \(\left(64a^3+125b^3\right)+55\left(16a^2-25b^2\right)\)

\(=\left[\left(4a\right)^3+\left(5b\right)^3\right]+55\left[\left(4a\right)^2-\left(5b\right)^2\right]\)

\(=\left(4a+5b\right)\left(16a^2-20ab+25b^2\right)+55\left(4a-5b\right)\left(4a+5b\right)\)

\(=\left(4a+5b\right)\left(16a^2-20ab+25b^2+220a-275b\right)\)

e) \(1-\left(x^2-2xy+y^2\right)\)

\(=1^2-\left(x-y\right)^2\)

\(=\left(1-x+y\right)\left(1+x-y\right)\)