Video Transcript
Expand negative 𝑥 plus two 𝑦 all
squared.
In this question then, we have a binomial
expression, negative 𝑥 plus two 𝑦. And we are squaring it. That means we’re multiplying this
binomial by itself. So, we’re looking for the result of
multiplying negative 𝑥 plus two 𝑦 by negative 𝑥 plus two 𝑦. There are numerous different methods that
we can use. In this question, I’m going to choose to
use the FOIL method. Now, we just need to be a little bit
careful because one of the terms in our binomial is negative. And we don’t want to let this trip us
up. We need to be really careful with the
signs when we’re multiplying each pair of terms together.
So, F, remember, stands for firsts. We multiply the first term in each
binomial together. That’s negative 𝑥 multiplied by negative
𝑥, which gives 𝑥 squared. Remember, a negative multiplied by a
negative gives a positive. Then, the letter O stands for outers or
outsides. We multiply the terms on the outside of
our expansion. That’s the negative 𝑥 in the first
binomial by the positive two 𝑦 in the second, giving negative two 𝑥𝑦. I stands for inners or inside. So, we multiply the terms in the center
of our expansion. That’s the two 𝑦 in the first binomial
and the negative 𝑥 in the second, giving another lot of negative two 𝑥𝑦. Finally, the letter L stands for lasts,
so we multiply the last term in each binomial together. That’s positive two 𝑦 multiplied by
positive two 𝑦, which is four 𝑦 squared.
So, after completing all four of our
multiplications, we now have four terms in our expansion, 𝑥 squared minus two 𝑥𝑦 minus
two 𝑥𝑦 plus four 𝑦 squared. Remember, there should always be two
identical terms in the center of our expansion. And indeed, there are. We have negative two 𝑥𝑦 minus another
lot of two 𝑥𝑦. We can therefore simplify our expansion
by grouping like terms, and we have our final answer to the problem. The simplified expansion of negative 𝑥
plus two 𝑦 all squared is 𝑥 squared minus four 𝑥𝑦 plus four 𝑦 squared.
