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

\(20x^2-32x=4x(5x-8)\)

\(20xy+28x=4x(5y+7)\)

\(12ab+27ac=3a(4b+9c)\)

\(12pqr+32pq=4pq(3r+8)\)

\(21x^3+24x^5=3x^3(7+8x^2)\)

\(8p^3+9p+p^6=p(8p^2+9+p^5)\)

\(10x^2y-35xy^2=5xy(2x-7y)\)

\(a^2-121=(a-11)(a+11)\)

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

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

\(25a^{10}-4=(5a^5-2)(5a^5+2)\)

\(80x^2-5=5(16x^2-1)=5(4x-1)(4x+1)\)

\(75x^4-48x^2=3x^2(25x^2-16)=3x^2(5x-4)(5x+4)\)

\(p^4-16=(p^2-4)(p^2+4)=(p-2)(p+2)(p^2+4)\)

\(x^{15}-16x^3=x^3(x^{12}-16)=x^3(x^6-4)(x^6+4)=x^3(x^3-2)(x^3+2)(x^6+4)\)

\(a^8b^4-c^6=(a^4b^2-c^3)(a^4b^2+c^3)\)

\(a^2+13a+36=(a+9)(a+4)\)

\(a^2+a-72=(a-8)(a+9)\)

\(p^2-11p+28=(p-4)(p-7)\)

\(x^2-18x+81=(x-9)(x-9)\)

\(4x^3-60x^2+216x=4x(x^2-15x+54)=4x(x-9)(x-6)\)

\(x^{14}-16x^7+63=(x^7-7)(x^7-9)\)

\(x^2-17x=(x-8\frac{1}{2})^2-72\frac{1}{4}\)

\(x^2+x+1=(x+\frac{1}{2})^2-\frac{1}{4}+1\)

\(\text{}=(x+\frac{1}{2})^2+\frac{3}{4}\)

\(4x^2-16x-1=4(x^2-4x)-1\)

\(\text{}=4((x-2)^2-4)-1\)

\(\text{}=4(x-2)^2-16-1\)
\(\text{}=4(x-2)^2-17\)