Question

数学分解因式。x²-4mx+8mn-4n²和 x³-11x²+31x-21。

x²-4mx+8mn-4n²和 x³-11x²+31x-21 怎么做？谢谢！

Answer 1

答案：(x-2n)(x+2n-4m)；（x-7)(x-3)(x-1)
这两个题都要用到分组分解法，第一个把x²-4n²用平方差公式展开，中间两项提取公因式4m,然后在用提取公因式（x-2n)；第二题把11x²分成7x²和4x²即(x³-7x²）-(4x²-31x+21)=(x-7)x²-（4x-3)(x-7)=(x-7)(x²-4x+3)=(x-7)(x-3)(x-1)

Answer 2

x²-4mx+8mn-4n²=(x²-4mx+4m²)-(4m²-8mn+4n²)=(x-2m)²-4(m-n)²
=[(x-2m)+(2m-2n)][(x-2m)-(2m-2n)]=(x-2n)(x-4m-2n)
x³-11x²+31x-21=x³-x²-10x²+10x+21x-21=x²(x-1)-10x(x-1)+21(x-1)
=(x-1)(x²-10x+21)=(x-1)(x-3)(x-7)

Answer 3

x²-4mx+4m²=(x-2m)²
x²-4mx+8mn-4n²=x²-4mx+4m²-4m²+8mn-4n²
用以上方式来做，只给提示，这个很简单，还是自己做吧！

Answer 4

x²-4mx+8mn-4n²
=x²-4mx+4m²+8mn-4n²-4m²
=(x-2m)²-(2n-2m)²
=(x-2n)(x-4m+2n)
x³-11x²+31x-21
=(x-1)(x²-10x+21)
=(x-1)(x-3)(x-7)

Answer 5

x²-4mx+8mn-4n²
=(x-2n)(x+2n)-4m(x-2n)
=(x-2n)(x+2n-4m)

x³-11x²+31x-21
=x³-x²-10x²+10x+21x-21
=x²(x-1)-10x(x-1)+21(x-1)
=(x-1)(x-3)(x-7)

Answer 6

x²-4mx+8mn-4n² 因式分解后的答案：

（x-2n）（x-4m+2n）
x³-11x²+31x-21

= x³-3x²-8x²+24x+7x-21

= x²(x-3)-8x(x-3)+7(x-3)

=(x-3)( x²-8x+7)

=(x-3)(x-1)(x-8)

=(x-1)(x-3)(x-8).