I'm supposed to factor this completely but I don't even know where to start!

a^{2} ± 2ab + b^{2} = (a ± b)^{2}

a^{2} - b^{2} = (a - b)(a + b)

~~~~~~~~

4a^{2} + 12ab + 9b^{2} - 25c^{2} = [(2a)^{2} + 2 · 2 · 3ab + (3b)^{2}] - (5c)^{2} =

= (2a + 3b)^{2} - (5c)^{2} = **(2a + 3b - 5c)(2a + 3b + 5c)**