Question

Factorise : 4(x-y)^2-12(x-y)(x+y)+9(x+y)^2

Answer 1

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Answer 2

The answer to the factorisation is, (x+5y) (x+5y)

Given : The given algebraic expression is, 4(x-y)^2-12(x-y)(x+y)+9(x+y)^2

To find : The factorisation of the given algebraic expression.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to factorise the given algebraic expression)

Here, we will be using the necessary algebraic formula.

The algebraic expression = 4(x-y)²-12(x-y)(x+y)+9(x+y)²

Let,

(x-y) = a

(x+y) = b

So, the algebraic expression = 4a²-12ab+9b²

So,

= 4a²-12ab+9b²

= (2a)² - (2×2a×3b) + (3b)²

= (2a-3b)²

= [2(x-y) - 3(x+y)]² [Putting the values of a and b]

= (2x-2y-3x-3y)²

= (-x-5y)²

= [-1 × (x+5y)]²

= (-1)² × (x+5y)²

= 1 × (x+5y)²

= (x+5y) (x+5y)

(This cannot be further factorised. That's why, this will be considered as the final result.)

Hence, the answer to the factorisation is, (x+5y) (x+5y)