### Video Transcript

Simplify fully one plus root two
times four minus root two, giving your answer in the form 𝑎 plus 𝑏 root two, where
𝑎 and 𝑏 are integers. So what they’re telling you to do
basically is multiply these brackets together. And we’ve just seen an example of
that using the FOIL method, but they’re asking for the answer in a very specific
format. And they do intend to throw these
kinds of little twists into trying to throw you off the sense sometimes. 𝑎 plus 𝑏 root two, so this just
means an integer — so a whole number — plus some whole number times the square root
of two. So they’re not asking you for the
value of 𝑎 or 𝑏 particularly, they’re just asking you to represent your answer in
that kind of layout. Okay, let’s write out the question
and stop multiplying out the brackets.

So we’re gonna do one times four,
which gives us four. We’re then gonna do one lot of
negative root two, which is just negative root two. Then root two times four or four
lots of root two, they’re both positive number; so it’s gonna be a positive answer. And then we’ve got positive root
two times negative root two. So positive times negative is
gonna give us a negative answer and then we’ve got root two times root two. So I just really need that for the
moment, but we do know that root two times root two as we just saw is just two. So we’ve got four take away two in
terms of just normal rational numbers, and four take away two is two. And then we’re starting off with
negative root two. Well that really means there’s just
one of them. So it’s really negative one root
two, one lot of root two. And then we’re adding another four
lots of root two. So if we start off a negative one
on the number line and add four, we’re gonna go one, two, three, four steps up to
positive three.

So here’s our answer then, two
plus three root two. And this tallies with the format
that we’ve been asked to give the answer in. So in this case, 𝑎 would be two
and 𝑏 is the multiplier of the root two here would be equal to three. Just check the signs carefully. So we were asked for 𝑎 plus 𝑏
root two. Well we’ve got two plus three root
two. So we know that 𝑎 will be two and
𝑏 will be three. As I said before, they didn’t
actually ask for the value of 𝑎 and 𝑏. But in some questions, they do; so
at least you now know how to answer those sorts of questions as well.