1.
(x+y+3)(x+y+2)
(2x-3y+1)(2x-3y-1)
(x+y+3)2
(a-b-2)2
(x+y-7)(x-y+7)
(x+y+4)(x-y-4)
2.
(4x+3y-2)(4x+3y+5)
(4a-2b+3)2
(6x-y+4)2
(-2x+y+4)(2x+y+4)
(5x-2y+1)(5x+2y-1)
(a+3b-4)(a-3b-4)
1
x+y=Aとおく
(x+y+3)(x+y+2)
=(A+3)(A+2)
=A2+5A+6
=(x+y)2+5(x+y)+6
=x2+2xy+y2+5x+5y+6
2x-3y=Aとおく
(2x-3y+1)(2x-3y-1)
=(A+1)(A-1)
=A2-1
=(2x-3y)2-1
=4x2-12xy+9y2-1
x+y=Aとおく
(x+y+3)2
=(A+3)2
=A2+6A+9
=(x+y)2+6(x+y)+9
=x2+2xy+y2+6x+6y+9
a-b=Aとおく
(a-b-2)2
=(A-2)2
=A2-4A+4
=(a-b)2-4(a-b)+4
=a2-2ab+b2-4a+4b+4
y-7=Aとおく
(x+y-7)(x-y+7)
={x+(y-7)}{x-(y-7)}
=(x+A)(x-A)
=x2-A2
=x2-(y2-14y+49)
=x2-y2+14y-49
y+4=Aとおく
(x+y+4)(x-y-4)
={x+(y+4)}{x-(y+4)}
=(x+A)(x-A)
=x2-A2
=x2-(y2+8y+16)
=x2-y2-8y-16
2.
4x+3y=Aとおく
(4x+3y-2)(4x+3y+5)
=(A-2)(A+5)
=A2+3A-10
=(4x+3y)2+3(4x+3y)-10
=16x2+24xy+9y2+12x+9y-10
4a-2b=Aとおく
(4a-2b+3)2
=(A+3)2
=A2+6A+9
=(4a-2b)2+6(4a-2b)+9
=16a2-16ab+4b2+24a-12b+9
6x-y=Aとおく
(6x-y+4)2
=(A+4)2
=A2+8A+16
=(6x-y)2+8(6x-y)+16
=36x2-12xy+y2+48x-8y+16
y+4=Aとおく
(-2x+y+4)(2x+y+4)
=(-2x+A)(2x+A)
=-4x2+A2
=-4x2+(y+4)2
=-4x2+y2+8y+16
2y-1=Aとおく
(5x-2y+1)(5x+2y-1)
={5x-(2y-1)}{x+(2y-1)}
=(5x-A)(5x+A)
=25x2-A2
=25x2-(4y2-4y+1)
=25x2-4y2+4y-1
a-4=Aとおく
(a+3b-4)(a-3b-4)
=(a-4+3b)(a-4-3b)
=(A+3b)(A-3b)
=A2-9b2
=(a-4)2-9b2
=a2-8a+16-9b2
=a2-9b2-8a+16
