x的平方+2xy+y的平方-1=(x+y)^2-1=(x+y+1)(x+y-1)
a的平方b的平方-a的平方+2ab+1=(ab+1)^2-a^2=(ab+a+1)(ab-a+1)
x的平方-x-9y的平方-3y=(x+3y)(x-3y)-(x+3y)=(x-3y-1)(x+3y)
x的平方-y的平方-z的平方-2yz=(y-z)^2-x^2=(y-z+x)(y-z-x)
已知A=（x+2）（x-3）（x+4）（x-5）+49
求證：A為一個(gè)完全平方數(shù)
A=(x^2-x-6)(x^2-x-20)+49
=(x^2-x)^2-26(x^2-x)+120+49
=(x^2-x)^2-26(x^2-x)+169
=(x^2-x-13)^2
已知4X的平方+4xy+y的平方-4X-2y+1=0
求證：2x的平方+3xy+y的平方-x-y=0
4x^2+4xy+y^2-4x-2y+1=0
(2x+y)^2-2(2x+y)+1=0
(2x+y-1)^2=0
2x+y-1=0
2x^2+3xy+y^2-x-y
=(2x+y)(x+y)-(x+y)
=(2x+y-1)(x+y)
=0
x的三次方+x²y-xy²-y的3次方
=x^2(x+y)-y^2(x+y)
=(x^2-y^2)(x+y)
=(x+y)(x-y)(x+y)
=(x-y)(x+y)^2
ax²-bx²+bx-ax+a-b=x^2(a-b)-x(a-b)+(a-b)=(x^2-x+1)(a-b)
X²+6xy+9y²-16a平方+8a-1
=(x+3y)^2-(4a-1)^2
=(x+3y+4a-1)(x+3y-4a+1)
a的平方-6ab+12b+9b²-4a=(a-3b)^2-4(a-3b)=(a-3b-4)(a-3b)
a的四次方-2a的三次方+a²-9=(a^2-a)^2-9=(a^2-a+3)(a^2-a-3)
4a²x-4a²y-b²x+b²y
=4a^2(x-y)-b^2(x-y)
=(4a^2-b^2)(x-y)
=(2a+b)(2a-b)(x-y)
x²-2xy-xz+yz+y²=(x-y)^2-z(x-y)=(x-y-z)(x-y)