题目

用十字相乘法分解因式：（1）x²y²-xy-2 (2)x⁴+11x³y+18x²y²……
用十字相乘法分解因式：（1）x²y²-xy-2 (2)x⁴+11x³y+18x²y² (3)x⁴+4x²-5 (4)6m²n²-mn-12 （5）5-7（a+1)-6(a+1)² (6)4x⁴-(x-1)²

提问时间：2020-12-03

答案

x²y²-xy-2＝（xy-2)(xy+1)
1 -2
1 +1 (-2)X1+1X1=-1
x⁴+11x³y+18x²y²=x²(x²+11xy+18y²)=x²(x+9y)(x+2y)
1 9
1 2 9X1+2X1=11
x⁴+4x²-5=(x²+5)(x²-1)=(x²+5)(x+1)(x-1)
1 +5
1 -1 5X1 + (-1)X1=4
6m²n²-mn-12=(2mn-3)(3mn+4)
2 -3
3 +4 (-3)X3+2X4=-1
5-7（a+1)-6(a+1)²=[1-2(a+1)][5+3(a+1)]=(-2a-1)(3a+8)
1 -2
5 3 (-2)X5+1X3=-7
4x⁴-(x-1)²=(2x²)²-(x-1)²=(2x²+x-1)(2x²-x+1)=(2x-1)(x+1)(2x²-x+1)
2 -1
1 1 2X1+(-1)X1=1