甲、乙两名同学进行的因式分解:甲:x²-xy+4x-4y=(x²-xy)+(4x-4y)(分成两组)=x(x-y)+4(x-y)(直接提公因式)=(x-5y)(x+4)乙:a²-b²-c²+2bc=a²-(b²+c²-2bc)(分成两
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甲、乙两名同学进行的因式分解:甲:x²-xy+4x-4y=(x²-xy)+(4x-4y)(分成两组)=x(x-y)+4(x-y)(直接提公因式)=(x-5y)(x+4)乙:a²-b²-c²+2bc=a²-(b²+c²-2bc)(分成两
甲、乙两名同学进行的因式分解:
甲:x²-xy+4x-4y=(x²-xy)+(4x-4y)(分成两组)=x(x-y)+4(x-y)(直接提公因式)=(x-5y)(x+4)
乙:a²-b²-c²+2bc=a²-(b²+c²-2bc)(分成两组)=a²-(b-c)²(直接提公因式)=(a+b-c)(a-b+c)
请你在他们的解法的启发下,完成下面的因式分解:
(1)m³-2m²-4m+8;(2)x²-2xy+y²-9
甲、乙两名同学进行的因式分解:甲:x²-xy+4x-4y=(x²-xy)+(4x-4y)(分成两组)=x(x-y)+4(x-y)(直接提公因式)=(x-5y)(x+4)乙:a²-b²-c²+2bc=a²-(b²+c²-2bc)(分成两
(1)m³-2m²-4m+8
=(m³-2m²)-(4m-8)
=m²(m-2)-4(m-2)
=(m-2)(m+2)(m-2)
=(m+2)(m-2)²
(2)x²-2xy+y²-9
=(x-y)²-9
=(x-y+3)(x-y-3)
(1)m³-2m²-4m+8;
=m²(m-2)-4(m-2)
=(m-2)(m+2)(m-2)
=(m+2)(m-2)²
(2)x²-2xy+y²-9
=(x-y)²-9
=(x-y+3)(x-y-3)
1)原式=(m^3-2m^2)+〔-(4m+8)〕
=m^(m+2)+〔-4(m+2)〕
=(m^2-4)(m+2)
=(m+2)(m-2)(m+2)
=(m-2)(m+2)^2
2)原式=-〔3^2-(x²-2xy+y²)〕
=-〔3^2-(x-y)^2〕
=-(3+x-y)(3-x+y)
=(x-y+3)(x-y-3)
(1)m³-2m²-4m+8;
=m²(m-2)-4(m-2)
=(m²-4)(m-2)
=(m-2)(m+2)(m-2)
=(m+2)(m-2)²
(2)x²-2xy+y²-9
=(x-y)²-9
=(x-y+3)(x-y-3)