Question

Find the squre root of 25x^2-40xy+16y^2

Answer 1

Answer:

(52x2 - 40xy) + 24y2

STEP3:Trying to factor a multi variable polynomial

 3.1    Factoring    25x2 - 40xy + 16y2 

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

 Found a factorization  :  (5x - 4y)•(5x - 4y)

Detecting a perfect square :

 3.2    25x2  -40xy  +16y2  is a perfect square 

 It factors into  (5x-4y)•(5x-4y)

which is another way of writing  (5x-4y)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 :

(5x - 4y)2