x^2-4y^2+2x-4y

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x^2-4y^2+2x-4y
x^2-4y^2+2x-4y

x^2-4y^2+2x-4y
x^2-4y^2+2x-4y
=(x^2+2x+1)-(4y^2+4y+1)
=(x+1)^2-(2y+1)^2
=(x+1+2y+1)(x+1-2y-1)
=(x+2y+2)(x-2y)

x^2-4y^2+2x-4y
=x^2+2*1*x+1^2-4y^2-4y-1
=(x+1)^2-(4y^2+4y+1)
=(x+1)^2-[(2y)^2+2*2y*1y+1^2]
=(x+1)^2-(2y+1)^2
=[(x+1)+(2y+1)][(x+1)-(2y+1)]
=(x+1+2y+1)(x+1-2y-1)
=(x-2y)(x+2y+2)