Question

27x^2-90xy-75y^2 factorise it

Answer 1

27x2-90xy+75y2 

Final result :

3 • (3x - 5y)2

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "y2"   was replaced by   "y^2".  1 more similar replacement(s).

Step by step solution :

Step  1  :

Equation at the end of step  1  :

((27 • (x2)) - 90xy) + (3•52y2)

Step  2  :

Equation at the end of step  2  :

(33x2 - 90xy) + (3•52y2)

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   27x2 - 90xy + 75y2  =   3 • (9x2 - 30xy + 25y2) 

Trying to factor a multi variable polynomial :

 4.2    Factoring    9x2 - 30xy + 25y2 

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

 Found a factorization  :  (3x - 5y)•(3x - 5y)

Detecting a perfect square :

 4.3    9x2  -30xy  +25y2  is a perfect square 

 It factors into  (3x-5y)•(3x-5y)
which is another way of writing  (3x-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 :

3 • (3x - 5y)2

Answer 2

Hello Friends ✌
Here is u r Ans ➡

$= 27x {}^{2} - 90xy - 75y {}^{2}$

$= 3(9x {}^{2} - 30xy - 25y {}^{2} )$
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Hope This Helps u ☺.