An algebra problem by Kidus Gebreyohannes

$4444444444^{2} = (4 \times 1111111111)^{2} =$ $4^{2} \times 111111111^{2} = 16 \times 111111111^{2}$ From there it's a matter of multiplication. $1111111111 \times 1111111111 =$ $1 \times 1111111111 + 10 \times 1111111111 + 100 \times 1111111111 ... +1000000000 \times 1111111111 = 123456700987654321$ $1234567900987654321 \times 16 = 1234567900987654321 \times 10 + 1234567900987654321 \times 6 = 12345679009876543210 + 07407407405925925926 = \boxed{19753086415802469136}$