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7(𝑥 − 2𝑦)^2 − 25(𝑥 − 2𝑦) + 12

Answer:

7(𝑥 − 2𝑦)^2 − 25(𝑥 − 2𝑦) + 12

Let us consider x – 2y = z

So we get,

= 7𝑧^2 − 25𝑧 + 12

We can further write it as

= 7𝑧^2 − 21𝑧 − 4𝑧 + 12

By taking out the common terms

= 7z (z – 3) – 4 (z – 3)

= (7z – 4) (z – 3)

Let us replace z by x – 2y

So we get,

7(𝑥 − 2𝑦)^2 − 25(𝑥 − 2𝑦) + 12

Then,

= (7(x – 2y) – 4) ((x – 2y) – 3)

= (7x – 14y – 4) (x – 2y – 3)

"hello everyone i am sumanjali math tutor
from leader learning welcome to question
answer session
given expression is 7 into x minus 2 y
whole square
minus 25 into x minus 2 y
plus 12 we need to factorize this
expression
factorization is nothing but we need to
express
this in terms of simple terms or product
of
factors okay so first of all as
as this expression is a bit complicated
with the terms x minus 2y isn't
it now so let us take in place of x
minus 2y
so let us take a value z
okay a value z
okay so the expression can be written as
7 into z square in place of x minus 2y
i'm writing
z minus 25 into z
plus 12 okay plus 12 and
as a step 1 in the process of
factorization the step one is we need to
take the product of
a and c a value will be coefficient of
x square and c value will be constant so
the coefficient of
yeah x square or z square it is 7
multiplied by 12 7 12 are 84
and we need to search an another pair of
factors for
84 that is 21 forza
21 forcer so that we can get the value
of by adding or subtracting this we can
get the value of
uh we can get the value of 25 okay
so we can write minus 25 z
as minus 21x
21z minus 4z
okay so this is 7z square
minus 21z minus
4 z plus 12 i am taking common
seven z from the first two terms okay
so the first term will be z if we take
seven z
common z will remains minus three will
be remains in the second
term and i am taking common the second
from the second pair of two terms minus
four
so that z will be remains in the first
term and minus three will be as the
fourth raiser 12
minus into minus plus so z minus 3 will
be reminds
so we can express this as a z minus 3
if we take common that 7 z minus
4 will reminds okay so the term
the equation 7 z square minus
25 z plus 12
can be written as z minus 3
into 7 z minus 4
so the factors of the given expression
is these two
and if we write in terms of x minus 2 by
7 minus
7 into x minus 2 y whole square minus 25
into
x minus 2 y plus 12
as so that in place of z value i am
writing
x minus 2 y minus 3
into 7 into x
minus 2 y minus
4 okay so these are the factors for the
given expression
okay that's all hope you understand if
you have further questions reach us at
comment section
and subscribe to the channel leader
learning for further queries
thank you
"

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