1.（ax+by)²+（bx－ay)²
= a²x²+2abxy+b²y²+b²x²-2abxy+a²y²
=a²x²+b²y²+b²x²+a²y²
=x²(a²+b²)+y²(a²+b²)
=(x²+y²)(a²+b²)
2.(x²-x)²-4(x²-x-1)
=x4-2x³+x²-4x²+4x+4
=x4-2x³-3x²+4x+4
=x²(x²-2x-3)+4(x+1)
=x²(x-3)(x+1)+4(x+1)
=(x+1)(x³-3x²+4)
3.4(x+y)²-9(x-y)²
=(2x+2y)²-(3x-3y)²
=(2x+2y+3x-3y)(2x+2y-3x+3y)
=(5x-y)(5y-x)
4.(a+b)(a-b)+4(b-1)
=a²-b²+4b-4
=a²-（b²-4b+4）
=a²-（b-2)²
=(a+b-2)(a-b+2)
5.x²+4xy+4y²-2x-4y-3
=(x+2y)²-2(x+2y)-3
=(x+2y-3)(x+2y+1)
6.(x+1)(x+2)(x+3)(x+4)+1
=(x²+3x+2)(x²+7x+12)+1
=x4+7x³+12x²+3x³+21x²+36x+2x²+14x+24+1
=x4+10x³+35x²+50x+25
=x²(x²+10x+25x)+10x²+50x+25
=x²(x+5)²+10x(x+5)+25
=[x(x+5)+5]²
=(x²+5x+5)²
7.3x²-11x+10
=(3x-5)(x-2)