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G= -x^2 - 2xy - y^2
K= x^2 + 4y^2 + 4xy
H= 4x^2 - 12xy + 9y^2
L= 25 - 10 + y^2
M= 10y^4 + 25x^6 +y^8

Sagot :

Answer:

Step-by-step explanation:

I am assuming you want to factor these functions

G= -x^2 - 2xy - y^2

  =  -(x^2 + 2xy + y^2)

We need 2 terms whose product is y^2 and whose sum is +2xy

- they are  + x and + y

  = - (x + y)(x + y)

  = -(x + y)^2

The other functions are worked out in the same way:

K =  x^2 + 4y^2 + 4xy

  = (x  + 2y)(x + 2y)

  = (x + 2y)^2

H = 4x^2 - 12xy + 9y^2

   = (2x - 3y)^2

L= 25 - 10 + y^2

 = (5 - y)^2

M =  10y^4 + 25x^6 +y^8

    - this is prime  (no factors)

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