Hey guys in this tutorial you're going to learn another technique for solving
or simplifying algebraic expressions called expanding it's a pretty useful
technique to manipulate equations that involve brackets so let's just have a
look at a normal expression that doesn't have any algebra so let's have a look at
five times bracket two plus three now if you remember our first tutorial we said
that whatever is inside brackets needs to be completed first
so 2 plus 3 is 5 so therefore we have 5 times 5 which is 25 now the funny
thing is this expression can be rewritten the same way if we try our
expanding technique which is when we have a number in front multiply by a
number of terms in the brackets we can simply get the number in front and
multiply each term separately on the inside and get the same result so let's
try doing that 5 times 2 plus 5 times 3 and that becomes 10 plus 15 which is 25
again so how is this possible well it makes sense because if you think of it 5
times 5 if you think about it 5 times 5 is the same thing as 5 plus 5 Plus 5
Plus 5 plus 5 now 5 times 2 is the same thing as 5 plus 5 and 5 times 3 is the
same thing as five plus five plus five so when you
have a plus in the middle if you plus them together it's exactly the same
thing as five times five so that's why this technique works so expanding is
simply the process of getting the number in front of the bracket and multiply
each term inside the bracket and that way you don't have to write the brackets
anymore now let's apply this technique to an algebraic equation so let's try it
to five times two plus X now there is actually no way for you to solve it
normally as you did with the numbers right because there's no way for you to
figure out what 2 plus x equals so therefore the only thing you can do is
expanding which means getting a number getting the term in front multiply by
each term on the inside so 5 times 2 is 10 5 times X is 5x so you have just
expanded this equation now let's try expanding a couple of other equations
expand the following
okay so let's try expanding these equations we have five x x is 5 x 5
times 3 is 15 you have 6 times X which is 6 X 6 times negative 2 is negative 12
so you have to be careful when you have a minus sign in the middle if you have a
minus sign in the middle the sign stays with the number after the sign so
instead of going 6 times 2 you actually do 6 times negative 2 which makes it
negative 12 now let's try this third one we have 2x times X is 2x squared 2x
times y is 2xy and the last one x squared times X is X cubed x squared
times negative 3 is minus 3x squared so obviously you need to be pretty familiar
with multiplying terms in algebra in order to do these questions if you've
forgotten how to multiply in algebra have a look at lesson 2 again on
simplifying algebraic equations ok thanks for watching this tutorial see
you next time.