 | ①
x^2-1/4+6yx+9y^2
=(x^2+6xy+9y^2)-1/4
=(x+3y)^2-(1/2)^2
=(x+3y+1/2)(x+3y-1/2)
②
a^2+ab+3a+2b+2
=(a+2)b+(a^2+3a+2)
=(a+2)b+(a+2)(a+1)
=(a+2)(a+b+1)
③
(x^2+2x)(x^2+2x-18)+45
=(x^2+2x-9+9)(x^2+2x-9-9)+45
=(x^2+2x-9)^2-9^2+45
=(x^2+2x-9)^2-6^2
=(x^2+2x-15)(x^2+2x-3)
=(x-3)(x+5)(x+3)(x-1)
④
xy-x+y-1
=(y-1)x+(y-1)
=(x+1)(y-1)
となります。
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