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How do I expand (3x + 6)(x + 2) ?

Firstly, this is a classic GCSE question that crops up time and again, so it's worth making sure that you can expand brackets blindfolded and with your arms tied behind your back before you walk into the exam. These can be easy marks in the bag every time and once you've got the hang of it, they're not too difficult.

The trick to expanding brackets is to always remember FOIL. That's First, Outside, Inside and Last. Now what does that mean? I hear you ask. Well each of the letters in FOIL refer to a different pair of numbers in the bracket.

The F stands for First. What this means is that you need to multiply the first numbers in the brackets together. The first thing in the first bracket is 3x and the first thing in the second bracket is x, so multiply these together to get 3x^2.

The O stands Outside. If we think of the brackets together now, we can see that there are two things on the outside of the brackets, and that is the 3x and the 2. We now multiply these together to get 6x.

The I stands for Inside. Just as we did for the Outside numbers, we imagine the two brackets as one thing, but this time we take the two Inside numbers. In our example, this is 6 and x. Multiply these two together to get 6x.

Finally, L stands for Last. Remember when we multiplied the the First two numbers in each bracket together? Now we just multiply the Last two numbers in each bracket together. Here they are 6 and 2, so we multiply them to get 12.

Now we have our four numbers, we simply add them all together to get our result:

(3x + 6)(x + 2) = F + O + I + L

=3x^2 + 6x + 6x + 12

=3x^2 + 12x + 12

That's the trick to expanding brackets. Just follow the simple steps every time and you've got full marks every time!

Joshua B. GCSE Maths tutor, A Level Maths tutor, A Level Further Math...

2 years ago

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