\(x^2+x=x(x+1)\)

\(9a^2+24a=3a(3a+8)\)

\(16pq+18p=2p(8q+9)\)

\(8ab+18ac=2a(4b+9c)\)

\(6xyz+15xy=3xy(2z+5)\)

\(35p^4+40p^2=5p^2(7p^2+8)\)

\(2x^3+9x^8+x^2=x^2(2x+9x^6+1)\)

\(24x^3y+27x^4y^3=3x^3y(8+9xy^2)\)

\(a^2-49=(a-7)(a+7)\)

\(36a^2-25=(6a-5)(6a+5)\)

\(81-64a^2=(9-8a)(9+8a)\)

\(121p^{12}-49=(11p^6-7)(11p^6+7)\)

\(75a^2-12=3(25a^2-4)=3(5a-2)(5a+2)\)

\(45x^4-20x^2=5x^2(9x^2-4)=5x^2(3x-2)(3x+2)\)

\(x^{12}-16=(x^6-4)(x^6+4)=(x^3-2)(x^3+2)(x^6+4)\)

\(3a^{13}-243a=3a(a^{12}-81)=3a(a^6-9)(a^6+9)=3a(a^3-3)(a^3+3)(a^6+9)\)

\(x^6y^{10}-100z^{10}=(x^3y^5-10z^5)(x^3y^5+10z^5)\)

\(x^2+9x+20=(x+4)(x+5)\)

\(x^2+5x-36=(x+9)(x-4)\)

\(a^2-8a+7=(a-1)(a-7)\)

\(a^2+6a+9=(a+3)(a+3)\)

\(5p^5+40p^4+35p^3=5p^3(p^2+8p+7)=5p^3(p+7)(p+1)\)

\(a^{10}+2a^5-63=(a^5-7)(a^5+9)\)

\(x^2-14x=(x-7)^2-49\)

\(x^2+8x+14=(x+4)^2-16+14\)

\(\text{}=(x+4)^2-2\)

\(3x^2-18x-1=3(x^2-6x)-1\)

\(\text{}=3((x-3)^2-9)-1\)

\(\text{}=3(x-3)^2-27-1\)
\(\text{}=3(x-3)^2-28\)