2（x^2-y^2）-x+y因式分解2（x^2-y^2）-x+y（a-b）^2+2a-2b+13mp^2+12mpq+12q^2(x+y)^2+4(x-y)^2-4(x^2-y^2)因式分解,

Question

2（x^2-y^2）-x+y因式分解
2（x^2-y^2）-x+y
（a-b）^2+2a-2b+1
3mp^2+12mpq+12q^2
(x+y)^2+4(x-y)^2-4(x^2-y^2)
因式分解,

Answer 1

2(x²-y²)-x+y
=2(x+y)(x-y)-(x-y)
=(x-y)[2(x+y)-1]
=(x-y)(2x+2y-1)
(a-b)²+2a-2b+1
=(a-b)²+2(a-b)+1
=[(a-b)+1]²
=(a-b+1)²
3mp²+12mpq+12mq² (如果式子是这样的话,最后一项是12mq²)
=3m(p²+4pq+4q²)
=3m(p+2q)²
(x+y)²+4(x-y)²-4(x²-y²)
=(x+y)²-4(x²-y²)+4(x-y)²
=(x+y)²-4(x+y)(x-y)+4(x-y)²
=[(x+y)-2(x-y)]²
=(x+y-2x+2y)²
=(3y-x)²