How do you multiply out two brackets?

Let us use the example of (x + 3)(x + 5)

The main thing we have to remember is to multiply every term in the first bracket by every term in the second bracket. An easy way to make sure we've done this is to use the F.O.I.L method of multiplying brackets. 

Firsts = x * x = x²

Outsides = x * 5 = 5x

Insides = 3 * x = 3x

Lasts = 3 * 5 = 15

If we now put these together we get : x² + 5x +3x + 15 = x² + 8x +15