Expand and Simplify (x+3)(x+5)

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You can multiply BOTH of the terms in the first bracket
by EACH of the terms in the second bracket.
I teach this as FOIL: Multiply the FIRST things in each bracket, then the OUTSIDE things, then the INSIDE things, then the LAST things of each bracket.
THEN, collect like terms, which means add/subtract the terms that just have ''x' in them.
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Let's see if I can remember this ..
(x + 3)(x + 5)
Well ..
It's x times x which is x^2
and it's 3 times 5 which is 15
but we mustn't forget the x times 3
and the x times 5 as well
Giving us x^2 + 3x + 5x + 15
and we can add the xs together
x^2 + 8x + 15
and I think that's as far as we can go.

MrMousley