a) \(\left(x+1\right)^4-\left(x-1\right)^4=\left[\left(x+1\right)^2\right]^2-\left[\left(x-1\right)^2\right]^2\)
\(=\left[\left(x+1\right)^2-\left(x-1\right)^2\right].\left[\left(x+1\right)^2+\left(x-1\right)^2\right]\)
\(=\left(x+1-x+1\right)\left(x+1+x-1\right)\left(x^2+2x+1+x^2-2x+1\right)\)
\(=2.2x.\left(2x^2+2\right)=8x\left(x^2+1\right)\)
b) \(\left(x^2-25\right)^2-4\left(x+5\right)^2=\left[\left(x-5\right)\left(x+5\right)\right]^2-4\left(x+5\right)^2\)
\(=\left(x+5\right)^2\left[\left(x-5\right)^2-4\right]=\left(x+5\right)^2\left(x^2-10x+25-4\right)=\left(x+5\right)^2\left(x^2-10+21\right)\)
\(=\left(x+5\right)^2\left(x-3\right)\left(x-7\right)\)
