\(5a^3-10a^2b+5ab^2-10a+10b\)
\(=5a\left(a^2-2ab+b^2\right)-5\left(2a-2b\right)\)
\(=5a\left(a-b\right)^2-5\left(2a-2b\right)\)
\(=5\left[a\left(a-b\right)^2-\left(2a-2b\right)\right]\)
\(=5\left[a\left(a-b\right)^2-2\left(a-b\right)\right]\)
\(=5\left(a-b\right)\left[a\left(a-b\right)-2\right]\)
\(x^6-x^4+2x^3+2x^2\)
\(=x^4\left(x^2-1\right)+2x^2\left(x+1\right)\)
\(=x^4\left(x-1\right)\left(x+1\right)+2x^2\left(x+1\right)\)
\(=\left[x^4\left(x-1\right)+2x^2\right]\left(x+1\right)\)
\(=\left[x^5-x^4+2x^2\right]\left(x+1\right)\)
\(=x^2\left(x^3-x^2+2\right)\left(x+1\right)\)
5a3-10a2b+5ab2-10a+10b
=5a.(a2-2ab+b2) - 10.(a-b)
=5a.(a-b)2-10.(a-b)
=5(a-b).[a.(a-b) - 2]
x6-x4+2x3+2x2
= x4.(x2-1)+2x2.( x+1)
= x4.(x+1).(x-1) +2x2.(x+1)
= x2.(x+1).[x2.(x-1) + 2]
= x2.(x+1).(x3-x2+2)
