Question

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

Answer 1

Let, (x + y) = a
(x - y) = b

××××××××××××××××

4b² - 12ab + 9a²

(2b)² - 2(6ab) + (3a)²

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By formula, (a - b)²=a²+b²-2ab
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(2b - 3a)²

=> [ 2(x - y) - 3(x + y)] ²

=> [ 2x - 2y - 3x - 3y]²

=> ( -x - 5y)² or (x + 5y)²

Factorized..

I hope this will help you

(-:

Answer 2

Given Equation is 4(x - y)^2 - 12(x - y)(x + y) + 9(x + y)^2

= > 4(x^2 - 2xy + y^2) - 12(x^2 - y^2) + 9(x^2 + y^2 + 2xy)

= > 4x^2 - 8xy + 4y^2 - 12x^2 + 12y^2 + 9x^2 + 9y^2 + 18xy

= > x^2 + 10xy + 25y^2

= > x^2 + 5xy + 5xy + 25y^2

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

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

= > (x + 5y)^2.


Therefore, Factorization of 4(x - y)^2 - 12(x - y)(x + y) + 9(x + y)^2 = (x + 5y)^2.



Hope this helps!