【分解因式】x²-9 x²-1 m²-n²

题目

【分解因式】x²-9 x²-1 m²-n²
【分解因式】
x²-9
x²-1
m²-n²
4a³-a
98-2x²
-4x²+25y²
49（x-y）²-9（y+x）²

答案

x²-9=(x+3)(x-3)
x²-1=(x+1)(x-1)
m²-n²=(m+n)(m-n)
4a³-a=a(4a-1)=a(2a+1)(2a-1)
98-2x²=-2(x²-49)=-2(x+7)(x-7)
-4x²+25y²=(5y+2x)(5y-2x)
49（x-y）²-9（y+x）²
=[7(x-y)]²-[3(x+y)]²
=[7(x-y)+3(x+y)][7(x-y)-3(x+y)]
=(10x-4y)(4x-10y)
=4(5x-2y)(2x-5y)