hi my name is mathematics and welcome to
this video
today i will be teaching you guys how to
expand and simplify
algebraic expressions so let's get into
it
before we get into the video you should
be familiar with these rules multiplying
positives and negatives so be confident
before you move into the video because
these are quite helpful
question one three open bracket x
plus y close bracket so
the first step you want to do is
multiply this positive 3
to this x so 3
times by x which equals to 3 x
because this is how expanding works
multiplying
variables or numbers that are inside the
bracket
and then three multiplied by y
positive y so three times by y equals to
three
y and then you can just
join join them together which will equal
to
3x plus by 3 y
and that is your answer question two
before we get into this question i want
you guys
to try this question out before i show
you the full
solution so i'll give you a few
seconds to solve this or you can pause
the video
so hopefully you guys paused the video
and tried this expression
so what you basically do is this
negative 4
multiplied to this positive 5 so
negative 4
times by positive 5 equals to negative
20 right and then
negative 4 times by negative
4a equals to positive 16.
now you're probably saying how's it
negative 16 because they're both
negatives a negative time by a negative
equals to a positive
so your final answer is going to be
negative 20 a
i mean sorry negative 20 plus by 16
a and let me just highlight that for you
question two is done let's move on to
question three
negative four open bracket x minus six
close bracket like we did in questions
one and two
we basically do the same step and
remember this is just a single
expanding this is not double so again
like we did in the uh the other two
questions we multiply this negative 4 to
this x
so anything that is outside the bracket
you multiply it
that is inside the bracket so
negative 4 times by x equals to negative
four x and negative four
times by negative six equals to positive
twenty four
now you're probably saying again how is
it negative i mean positive
twenty four because they're both
negatives negative times by negative
equals to positive
and then you can combine them together
so
negative 4x plus 24
and that is your final answer and i'm
gonna highlight that for you
so let's move on to a double brackets
question four double brackets two open
bracket
x plus y close bracket plus three
i mean open bracket x plus y closed
bracket
don't hesitate while looking at this
expression expression
because it's basically the same steps as
we did in number two
number one two and three we can
cut this in half and multiply all of
that
and multiply all of that so let's start
off with this one
first so two times by x equals two
to x and 2 times 5y
equals 2 to y
now let's do the 3 because the
2 this part is already done well before
we move on to that let's just combine
this it will be 2x plus by 2
y let's move on to this now so
3 open bracket x plus y close bracket
so 3 times by x equals to three
x and three times by
y equals to three y and let's just
combine them together
so three x plus by three
y and then this 3x is a positive
so we can just put a positive over here
and then we have to collect all the like
terms
so the like terms are 2x and positive 3x
so we can add them together and it's 2y
and 3y so we can add them together
so the answer is going to be 5x plus by
5y
done with number four let's move on to
number five
seven x sorry seven open bracket
x minus y close bracket positive two
open bracket x minus y close bracket
like we did in number four this is a
double expanding bracket
so we basically have to split it in half
and then
multiply it so let's move on to this one
seven open bracket x minus y so
seven times by x equals to seven
x and seven times by negative y
equals to negative seven y
and then let's combine them together so
it would be seven x minus seven y
so there's no negative here so if
there's no symbol in front
me that means it's going to be a
positive
if it says negative then that number is
a negative in front
so let's move on to to open bracket
x plus sorry x negative
y or closed bracket so
two times by x two times by x equals to
two x sorry about that
equals to two x and two times by
negative y equals two negative
two y and then let's combine them
together which would equal to
positive two x two x
minus two y now let's collect
all the like terms so we can get to our
final answer
so the like terms are 7x and
positive 2x so we can add them together
which would equal to
9x and then we have negative seven
y and negative two y which would equal
to
negative nine y and that is your final
answer
question six like we did in the other
questions
we split this in half because this is
the way this is how i
do my expanding brackets we i split it
in half and then multiply it
so 10 times by x equals to 10x
and 10 times by 4 equals to 40
and then we combine them together which
would equal to 10
x plus by 40. now let's move on to
this side so we have negative two
times by uh positive x so negative two
times by
x equals two negative two x
and then we have a negative two times by
negative eight which equals to
positive 16 you guys should already know
this
i showed you in the first part of the
video and then we can
combine them together so negative 2x
and then positive 16
and then we collect all the like terms
and then add or subtract them together
so we have positive 10x and negative 2x
so positive 10x minus 2x
negative 2x equals to 8x
and then we have positive 40
and positive 16 which equals to positive
56 and that is your final answer
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