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問27
(1)x^2+3xy+2y^2+5x+7y+6
=x^2+(3y+5)x+(2y^2+7y+6)
=x^2+(3y+5)x+(2y+3)(y+2)
={x+(2y+3)}{x+(y+2)}
=(x+2y+3)(x+y+2)

(2)2x^2-3xy-2y^2+x+3y-1
=2x^2-(3y-1)x-(2y^2-3y+1)
=2x^2-(3y-1)x-(2y-1)(y-1)
={2x-(y-1)}{x-(2y-1)}
=(2x-y+1)(x-2y+1)

問28
a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2)+2abc
=(b+c)a^2+(b^2+c^2+2bc)a+(b^2c+bc^2)
=(b+c)a^2+(b+c)^2a+bc(b+c)
=(b+c)(a^2+ab+ca+bc)
=(b+c){(a+c)b+a^2+ca}
=(b+c){(a+c)b+a(a+c)}
=(b+c)(a+c)(b+a)
=(a+b)(b+c)(b+a)
だと思います。

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