Simplifying
(2a + 3b)(5c + 7d)

Multiply (2a + 3b) * (5c + 7d)
(2a * (5c + 7d) + 3b * (5c + 7d))
((5c * 2a + 7d * 2a) + 3b * (5c + 7d))
((10ac + 14ad) + 3b * (5c + 7d))
(10ac + 14ad + (5c * 3b + 7d * 3b))
(10ac + 14ad + (15bc + 21bd))
(10ac + 14ad + 15bc + 21bd)