Question

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

Answer 1

Result:- (x + 5y)2

Equation at the end of step  1  : ((4•((x-y)2))-((12•(x-y))•(x+y)))+9•(x+y)2 Step  2  :Equation at the end of step  2  : ((4•((x-y)2))-(12•(x-y)•(x+y)))+9•(x+y)2 Step  3  :Equation at the end of step  3  : ((4•((x-y)2))-12•(x-y)•(x+y))+9•(x+y)2 Step  4  :Equation at the end of step  4  : (4•(x-y)2-12•(x-y)•(x+y))+9•(x+y)2 Step  5  : 5.1    Evaluate :  (x+y)2   =  x2+2xy+y2 Trying to factor a multi variable polynomial :

 5.2    Factoring    x2 + 10xy + 25y2 

Try to factor this multi-variable trinomial using trial and error 

 Found a factorization  :  (x + 5y)•(x + 5y)

Detecting a perfect square :

 5.3    x2  +10xy  +25y2  is a perfect square 

 It factors into  (x+5y)•(x+5y)
which is another way of writing  (x+5y)2

How to recognize a perfect square trinomial:  

 • It has three terms  

 • Two of its terms are perfect squares themselves  

 • The remaining term is twice the product of the square roots of the other two terms

Final result : (x + 5y)2

Answer 2

4 ( x - y )^ 2 - 12 (x-y) (x+y) + 9 (x+y)^2 ={2 (x-y)}^2-2×2 (x-y)×3 (x+y)+ {3 (x+y)}^2 ={(x-y)-(x+y)}^2 =(x-y-x-y)^2 =(-2y)^2 =4y^2