Question

factorise 4x² - 12xy + 9 y² plz find the answers ​

Answer 1

Without using Identity

4x² - 12xy + 9y²

4x² - 6xy - 6xy + 9y²

2x(2x - 3y) - 3y(2x - 3y)

(2x - 3y)²

Using Identity (a - b)² = a² - 2ab + b²

4x² - 12xy + 9y²

(2x)² - 2*2x*3y + (3y)²

(2x - 3y)²

Answer 2

$\sf{Answer:-}$

Step-by-step-explanation:-

Given to factorise 4x² - 12xy + 9y²

Factorisation

Finding factors:-

4x² - 12xy + 9y²

4x² × 9y² = 36x²y²

36x²y²

xy × 36xy = 36x²y²

2xy × 18xy = 36x²y²

3xy × 12xy = 36x²y²

4xy × 9xy = 36x²y²

6xy × 6xy = 36x²y²

9xy × 4xy = 36x²y²

12xy × 3xy = 36x²y²

18xy × 2xy = 36x²y²

36xy × xy = 36x²y²

Here we got factors their sum or subtraction should be equal to -12xy

-6xy - 6xy = -12xy & product is

-6xy × -6xy = 36x²y²

So, split middle term as -6xy-6xy

4x² - 12xy + 9 y²

4x² - 6xy -6xy + 9y²

Taking common

2x (2x -3y) -3y(2x -3y)

Again take common

(2x-3y) (2x-3y)

= (2x-3y)²

So,the factorised form of 4x² - 12xy + 9y² is (2x-3y)²

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Without explanation If u need u can see..

4x²-12xy + 9y²

4x² -6xy -6xy + 9y²

2x(2x-3y)-3y(2x-3y)

(2x-3y)(2x-3y)

(2x-3y)²

So , factorized form is (2x-3y)²