\(a^2+5a=a(a+5)\)

\(15x^2+21x=3x(5x+7)\)

\(15pq+35p=5p(3q+7)\)

\(15ab+20ac=5a(3b+4c)\)

\(4xyz+18xy=2xy(2z+9)\)

\(8a^2-10a^5=2a^2(4-5a^3)\)

\(2x^3-5x^2+x^5=x^2(2x-5+x^3)\)

\(25p^5q-40p^2q^3=5p^2q(5p^3-8q^2)\)

\(x^2-64=(x-8)(x+8)\)

\(81a^2-100=(9a-10)(9a+10)\)

\(81-4a^2=(9-2a)(9+2a)\)

\(121a^{10}-49=(11a^5-7)(11a^5+7)\)

\(80x^2-45=5(16x^2-9)=5(4x-3)(4x+3)\)

\(50p^4-18p^2=2p^2(25p^2-9)=2p^2(5p-3)(5p+3)\)

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

\(2p^{13}-162p=2p(p^{12}-81)=2p(p^6-9)(p^6+9)=2p(p^3-3)(p^3+3)(p^6+9)\)

\(x^8y^{12}-64z^{12}=(x^4y^6-8z^6)(x^4y^6+8z^6)\)

\(p^2+10p+24=(p+4)(p+6)\)

\(x^2+7x-18=(x-2)(x+9)\)

\(a^2-6a+5=(a-5)(a-1)\)

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

\(4x^4-16x^3-20x^2=4x^2(x^2-4x-5)=4x^2(x-5)(x+1)\)

\(x^6+12x^3+35=(x^3+5)(x^3+7)\)

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

\(x^2+16x+12=(x+8)^2-64+12\)

\(\text{}=(x+8)^2-52\)

\(2x^2+10x-9=2(x^2+5x)-9\)

\(\text{}=2((x+2\frac{1}{2})^2-6\frac{1}{4})-9\)

\(\text{}=2(x+2\frac{1}{2})^2-12\frac{1}{2}-9\)
\(\text{}=2(x+2\frac{1}{2})^2-21\frac{1}{2}\)