b) \(a^5+a^4+a^3+a^2+a+1\)
\(=a^4\left(a+1\right)+a^2\left(a+1\right)+a+1\)
\(=\left(a^4+a^2+1\right)\left(a+1\right)\)
c) \(x^3-1+5x^2-5+3x-3\)
\(=\left(x-1\right)\left(x^2+x+1\right)+5\left(x^2-1\right)+3\left(x-1\right)\)
\(=\left(x-1\right)\left[x^2+x+1+5\left(x+1\right)+3\right]\)
\(=\left(x-1\right)\left(x^2+6x+9\right)=\left(x-1\right)\left(x+3\right)^2\)
a) \(x^2+3ab\left(2-3ab\right)-10xy-1+25y^2\)
\(=\left(x^2-10xy+25y^2\right)+6ab-9a^2b^2-1\)
\(=\left(x-5y\right)^2-\left(9a^2b^2-6ab+1\right)\)
\(=\left(x-5y\right)^2-\left(3ab-1\right)^2\)
\(=\left(x-5y-3ab+1\right)\left(x-5y+3ab-1\right)\)
