Take your (b+3)(b-9) and assign the letters of FOIL to them using the following:
F: First For this, you are going to multiply the first quantity from each part of the binomial. The first quantity from (b+3) is b, and the first quantity from (b-9) is also b, so multiplying them gives us: b x b = b^2
I: Inside For this, you are going to multiply the inside quantity from each part of the binomial. Look at (b+3)(b-9) and think of which quantities would be characterized as the 'inside' of the binomial. You should get 3 from (b+3) and b from (b-9), as those are the inside quantities. Multiplying them gives us: 3 x b = 3b.
O: Outside For this, you are going to multiply the outside quantity from each part of the binomial. Look at (b+3)(b-9) and think of which quantities would be characterized as the 'outside' of the binomial. You should get b from (b+3) and -9 from (b-9), as those are the outside quantities. Multiplying them gives us: b x -9 = -9b
L: Last For this, you are going to multiply the last quantity from each part of the binomial. The last quantity from (b+3) is 3 and the last quantity from (b-9) is -9. Multiplying them gives us: 3 x -9 = -27
Simply add each answer together to get the final equation: b^2 + 3b - 9b - 27 Simplifying further gives us: b^2 - 6b - 27
