Question

- What is the complete factorization of 4x2 – 24xy + 36y2 ?​

Answer 1

Answer:

The complete factorization of $4 x^{2}-24 x y+36 y^{2}$ are 4(x-3y)(x+3y)

Solution:

Given Data:

$4 x^{2}-24 x y+36 y^{2}$

Take common value in all the three term.so we take 4 as common term in the above expression

$4 x^{2}-24 x y+36 y^{2}=4\left(x^{2}-6 x y+9 y^{2}\right)$

Now factorize the expression $\left(x^{2}-6 x y+9 y^{2}\right)$

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 $\times$ -3= 9  

-3 , -3 satisfies the condition.

So the expression will become as $x^{2}-6 x y+9 y^{2}$ = $x^{2}-3 x y-3 x y+9 y^{2}$

Take the common term

x(x-3y)+3y(x-3y)  

(x-3y)(x+3y)  

hence the complete factorization of $4 x^{2}-24 x y+36 y^{2}$ are 4(x-3y)(x+3y)