Question

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

Answer 1

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
`*` -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)