45 x ( 55 + 117 ) + 55 x ( 117 - 45 )
= (45 x 55 - 45 x 55) + (45 + 55) x 117
= 0 + 100 x 117 = 11700
\(45\times\left(55+117\right)+55\times\left(117-45\right)\)
\(=45\times55+45\times117+55\times117-55\times45\)
\(=\left(45\times55-45\times55\right)+45\times117+55\times117\)
\(=45\times117+55\times117\)
\(=117\times\left(45+55\right)\)
\(=117\times100\)
\(=11700\)