Question

因式分解

1、1+m+4分之m的二次方
2、-x²-4y²+4xy
3、-25x²-30xy-9y²
4、4（x-y）²+4（x-y）+1
5、（x-y）²+4xy

Answer 1

解
1+m+m²/4
=1²+2×m×(m/2)+(m/2)²
=(m/2+1)²

-x²-4y²+4xy
=-(x²-4xy+4y²)
=-(x-2y)²

-25x²-30xy-9y²
=-(25x²+30xy+9y²)
=-(5x+3y)²

4(x-y)²+4(x-y)+1
=[2(x-y)]²+2×1×(x-y)+1²
=[2(x-y)+1]²
=(2x-2y+1)²

(x-y)²+4xy
=x²-2xy+y²+4xy
=(x²+2xy+y²)
=(x+y)²