\(P=2a^3+7a^2b+7ab^2+2b^3\)
\(P=2a^3+2a^2b+5a^2b+5ab^2+2ab^2+2b^3\)
\(P=\left(2a^3+2a^2b\right)+\left(5a^2b+5ab^2\right)+\left(2ab^2+2b^3\right)\)
\(P=2a^2\left(a+b\right)+5ab\left(a+b\right)+2b^2\left(a+b\right)\)
\(P=\left(a+b\right)\left(2a^2+5ab+2b^2\right)\)
\(P=\left(a+b\right)\left[2a^2+4ab+ab+2b^2\right]\)
\(P=\left(a+b\right)\left[2a\left(a+2b\right)+b\left(a+2b\right)\right]\)
\(P=\left(a+b\right)\left(2a+b\right)\left(a+2b\right)\)