1.分解因式2a²-b²+ab-2a+b2.已知m=x-y,n=xy,试用m,n表示(x³+y³)².3.当x=-1时,x³+2x²-5x-6=0.请根据这一事实,将x³+2x²-5x-6分解因式.
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![1.分解因式2a²-b²+ab-2a+b2.已知m=x-y,n=xy,试用m,n表示(x³+y³)².3.当x=-1时,x³+2x²-5x-6=0.请根据这一事实,将x³+2x²-5x-6分解因式.](/uploads/image/z/13145375-47-5.jpg?t=1.%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8F2a%26%23178%3B-b%26%23178%3B%2Bab-2a%2Bb2.%E5%B7%B2%E7%9F%A5m%3Dx-y%2Cn%3Dxy%2C%E8%AF%95%E7%94%A8m%2Cn%E8%A1%A8%E7%A4%BA%EF%BC%88x%26%23179%3B%2By%26%23179%3B%EF%BC%89%26%23178%3B.3.%E5%BD%93x%3D-1%E6%97%B6%2Cx%26%23179%3B%2B2x%26%23178%3B-5x-6%3D0.%E8%AF%B7%E6%A0%B9%E6%8D%AE%E8%BF%99%E4%B8%80%E4%BA%8B%E5%AE%9E%2C%E5%B0%86x%26%23179%3B%2B2x%26%23178%3B-5x-6%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8F.)
1.分解因式2a²-b²+ab-2a+b2.已知m=x-y,n=xy,试用m,n表示(x³+y³)².3.当x=-1时,x³+2x²-5x-6=0.请根据这一事实,将x³+2x²-5x-6分解因式.
1.分解因式
2a²-b²+ab-2a+b
2.已知m=x-y,n=xy,试用m,n表示(x³+y³)².
3.当x=-1时,x³+2x²-5x-6=0.请根据这一事实,将x³+2x²-5x-6分解因式.
1.分解因式2a²-b²+ab-2a+b2.已知m=x-y,n=xy,试用m,n表示(x³+y³)².3.当x=-1时,x³+2x²-5x-6=0.请根据这一事实,将x³+2x²-5x-6分解因式.
1、2a^2-b^2+ab-2a+b=(a+b)^2+a^2-ab-2b^2-2a+b=(a+b)^2+(a+b)(a-2b)-2a+b
=(a+b)(2a-b)-(2a-b)=(2a-b)(a+b-1);从最高幂配方开始往下做,肯定能完成;
2、同样方法:x^3+y^3=x^3-2x^2y+xy^2+y^3+2x^2y-xy^2=x(x-y)^2+y(x-y)^2+xy(x+y)
=(x+y)((x-y)^2+xy);
所以,(x^3+y^3)^2=((x-y)^2+4xy)((x-y)^2+xy)^2;
由m=x-y, n=xy; 代入,得:(x^3+y^3)^2=(m^2+4n)(m^2+n)^2;
3、x=-1, 得,x+1=0; 所以将原式高次幂配成x+1的形式,然后往下做即可:
x^3+2x^2-5x-6=x(x+1)^2-6(x+1)=(x+1)(x^2+x-6)=(x+1)(x-2)(x+3);