(2x+y)^2-9(x+2y)^2

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(2x+y)^2-9(x+2y)^2

(2x+y)^2-9(x+2y)^2
(2x+y)^2-9(x+2y)^2

(2x+y)^2-9(x+2y)^2
(2x+y)^2-9(x+2y)^2
=(2x+y+3x+6y) (2x+y-3x-6y)
= (5x+7y)( -x-5y)
= -(5x+7y)( x+5y)


(2x+y)²-9(x+2y)²
=(2x+y)²-[3(x+2y)]²
=[(2x+y)-3(x+2y)][(2x+y)+3(x+2y)]
=(2x+y-3x-6y)(2x+y+3x+6y)
=(-x-5y)(5x+7y)
=-(x+5y)(5x+7y)

因式分
原式=[(2x+y+3(x+2y)]*{(2x+y-3(x+2y)].
=(5x+7y)(-x-5y).
=-(5x+7y)(x+5y).