This week I learnt how to use an area model to expand an expression. It’s very useful since it organizes everything so you don’t miss a step while multiplying terms. Heres an example:

Draw a lowercase T and divide the bottom and right according to the number of terms in the expression. Since a binomial is being multiplied by a trinomial, the top is divided in two and the sides are divided in three.

Now plug the numbers into their corresponding spots:

Then, you simply multiply the numbers together! You can almost think of it like playing battleship:

I have colour coded all the like terms together. The ones that are the same colour are added together, and the final answer is .

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This week, I got half of the question correct, since my final answer was . However, the actual answer was and I could not figure out why. While I was going over the homework with my friends and discussing this one question, the solution suddenly popped into my head and the question finally made sense!

I had been adding and multiplying the exponents together, but that was only half the battle:

But the exponent meant that the binomial is multiplying by itself, so using distribution to solve the problem is the correct way to do it:

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