Unknown: Welcome to R&H Academy
channel. Question two of
exercise 2.5 says, evaluate the
following products without
multiplying directly. First part
is 103 multiply 107 . 103 can be
expressed as 100 plus three
and 107 can be expressed as 100
plus seven.
Remember the identity expressing
multiply x plus b equal to x
square plus a plus b multiply x
plus ab.
x is hundred
A is three B IS seven x is 100
three multiply 7. 100 Square is
10,000
plus three plus seven is 10
multiply 100
plus seven multiply three is 21.
10 multiply 100 is 1000
plus 21 are the three terms
103 multiply 107 is 11,021.
Let's move to second part.
Second part is 95 multiply 96.
95 can be expressed as
100 minus 5. 96 can be expressed
as hundred minus four
Now bit similar to x plus a
multiply x plus b, use the
identity. In this case, x is
hundred, A is
minus five and B is minus four,
substitute the terms in the
identity. X is hundred.
A is minus five,
B is minus four,
x is hundred, plus
A multiply B
hundred square is 10,000
minus five minus four is minus
nine, multiply 100
minus Five multiply minus four
is
plus 20.
minus nine multiply 100 is minus
900
plus 20 .   10,000 minus 900
plus 20 is 9120. Let's move to
the third part 104 can be
written as hundred, plus four,
and 96 can be expressed as
hundred minus four. Now again we
can use the identity
used in a previous part, but we
will use another identity, we
will use the identity A plus B
multiply  A minus B.
A is hundred
four
substitute these terms,
hundred square
minus
four square, hundred square is
10,000. 4 square is 16.   1000
minus 16 is
What should question three is
factorize the following using
appropriate identities, nine x
square can be expressed as three
x whole square y square as
six xy can be expressed as two
multiply
3 x multiply
one
so nine x square plus 6xy plus y
square can be expressed as
we'll use the identity
a square plus 2ab plus b square
is equal to a plus b whole
square. Now a is three x.
b is y
substituting these values in a
plus b whole square again
three x plus y whole square two
factors of nine x square plus
six x y plus y square are three
x plus y multiply three x plus
y. Second part is four y square
minus four, plus one for y
square can be expressed as, two
y whole square. and one can be
expressed as one square, which
is equal to one.
Now, four y can be expressed as
two
multiply two y multiply,
one.
Four y square minus four y plus
one can be expressed as
a square plus b square minus two
ab equal to a minus b whole
square
a is
two y and b is one, substitute
the terms in a minus b whole
square
two y minus one whole square.
So, factors are two y minus one
and two y minus one. x square
minus y square by 100. Now, it
is a bit similar to a square
minus b square
which is equal to a minus b
multiply a  plus b
a is x and b is y by ten
,  in this case, substitute the
terms in the identity.
Remember, a square is equal to x
square, so a will be x.
Similarly, b square is y square
by 100. So b will be
y by 10
a is x   b is y by 10.
x plus y by 10.
So, this brings us to an end of
question three as well. In
question three we have used
these three identities, make
sure that you remember them to
solve next
See you in the next video.
