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Factorise:

9 x^{2} y^{2}-16

Answer:

Solution:

The factorization is substantially simpler when certain identities are used.

Many expressions that need to be factored have the form of or can be put into the form of: a^{2} - b^{2} = ( a+b)(a-b)

\begin{array}{l} =(3 x y)^{2}-4^{2} \\ =(3 x y-4)(3 x y+4) \\ \text { Using Identity: } x^{2}-y^{2}=(x+y)(x-y) \end{array}

"hello students i am rita your master
tutor and the today's question is
factorize 63 a square minus
112 v square first of all we have to
make
these two numbers is a perfect square
then so 63 and 112 both are
not a perfect square of any number so
first of all we find
the hcf of at cf
of 63 and 112
it means first of all we have to find
the highest common factor of 63 and 112
so we find the hcf of 63 and 112 then it
becomes 63
63 12 minus 3 9 10 minus 6 4
now 49 ones are 49 39 13 minus 9
4 5 minus 4 1 and then
14 3's are 42 9 minus two seven
and then seven to the fourteen it means
the highest
common factor is seven
so we take out seven common from these
two number
seven nines are sixty three a square
minus seven when the seven forty two
seven six of forty two now this become
a perfect square because nine is a
perfect
square of 3 and a square is a perfect
square of 8 and 16 is a perfect square
of
4 now it becomes a perfect square
now we use the identity of
x square minus y square now we use the
identity of
x square minus y square and the identity
of x
square minus y square is x plus y
into x minus y now we use this identity
in this question and we got the answer
that is 7
3 a minus 4 b
and 3 a plus 4
b so this is the answer of this question
7 bracket 3a minus 4b and 3a plus 4v
so this is the answer and we use this
identity in this question
i hope you like this video so please
subscribe video for more updates and do
comment your questions thank you
"

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