Math, asked by arjunsaneesh5794, 11 months ago

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

Answers

Answered by dharaneeshtummala13
1

Answer:

Step-by-step explanation:

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

Answered by PraaneshNair
0

Answer:

4(x-y)² - 12(x-y)(x+y) + 9(x+y)²

= 4(x² -2xy + y²) - 12(x² - y²) + 9(x² + 2xy + y²)

= 4x² - 8xy + 4y² - 12x² + 12y² + 9x² + 18xy + 9y².

= 17x² + 10xy + 25y²

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