Answer:
The complete factorization of [tex]4 x^{2}-24 x y+36 y^{2}[/tex] are 4(x-3y)(x+3y)
Solution:
Given Data:
[tex]4 x^{2}-24 x y+36 y^{2}[/tex]
Take common value in all the three term.so we take 4 as common term in the above expression
[tex]4 x^{2}-24 x y+36 y^{2}=4\left(x^{2}-6 x y+9 y^{2}\right)[/tex]
Now factorize the expression [tex]\left(x^{2}-6 x y+9 y^{2}\right)[/tex]
Find the two numbers, whose product should be 9 and sum should be -6.
-3,-3 are the numbers which satisfy the above condition.
When we add -3-3=Sum is 6
Product of -3 [tex]\times[/tex] -3= 9
-3 , -3 satisfies the condition.
So the expression will become as [tex]x^{2}-6 x y+9 y^{2}[/tex] = [tex]x^{2}-3 x y-3 x y+9 y^{2}[/tex]
Take the common term
x(x-3y)+3y(x-3y)
(x-3y)(x+3y)
hence the complete factorization of [tex]4 x^{2}-24 x y+36 y^{2}[/tex] are 4(x-3y)(x+3y)