Question

几题因式分解

1.9-6xy+x^2y^2 2.(a+b)^2-18(a+b)+81
3.4-12(m-n)+9(m-n)^2 4.x^3-1
5.1-1/8a^3 6.-a-8a^4
7.x^2+7x+10 8.y^2-7x+12
9.a^2x^2+ax-8 10.x^4-7x^2-18
11.2x^2-7x-15 12.5a^2+7a-6
13.x^4-4x^3+4x^2-9 14.x^2(x-y)+y-x
15.a^2(a^2-1)-4a^2+4 16.5x^3-2x^2y+8y-2ax

Answer 1

【不好意思，看到时太晚了】
1）9-6xy+x^2y^2
=(xy)²-2×3×xy+3²
=(xy-3)²

2）(a+b)^2-18(a+b)+81
=(a+b)²-2×9×(a+b)+9²
=(a+b-9)²

3）4-12(m-n)+9(m-n)^2
=[3(m-n)]²-2×2×3(m-n)+2²
=[3(m-n)-2]²
=(3m-3n-2)²

4）立方差公式：a³-b³=(a-b)(a²+ab+b²)
x^3-1
=x³-1³
=(x-1)(x²+1×x+1²)
=(x-1)(x²+x+1)

5）1-1/8a^3
=1³-(½a)³
=(1-½a)[1²+1×½a+(½a)²]
=(1-½a)(1+½a+1/4 a)

6）立方和公式：a³+b³=(a+b)(a²-ab+b²)
-a-8a^4
=-a(1+8a³)
=-a[1³+(2a)³]
=-a(1+2a)[1²-1×2a+(2a)²]
=-a(1+2a)(1-2a+4a²)

7）.x^2+7x+10
=(x+2)(x+5)

8）y^2-7x+12
=(y-3)(y-4)

9）题目似乎错了，应是a^2x^2+2ax-8吧
a^2x^2+2ax-8
=(ax)²+2ax-8
=(ax-2)(ax+4)

10）x^4-7x^2-18
=(x²)²-7x²-18
=(x²-9)(x²+2)
=(x+3)(x-3)(x²+2)

11）5a^2+7a-6
=(5a-3)(a+2)

12）2x^2-7x-15
=(2x+3)(x-5)

【7-12为十字相乘，故无详细过程】

13）x^4-4x^3+4x^2-9
=(x^4-4x³+4x²)-9
=x²(x²-4x+4)-9
=x²(x-2)²-9
=[x(x-2)]²-3²
=(x²-2x+3)(x²-2x-3)
=(x²-2x+3)(x-3)(x+1)

14）x^2(x-y)+y-x
=x²(x-y)-(x-y)
=(x-y)(x²-1)
=(x-y)(x+1)(x-1)

15）a^2(a^2-1)-4a^2+4
=a^4-a²-4a²+4
=a^4-5a²+4
=(a²-1)(a²-4)
=(a-1)(a+1)(a-2)(a+2)

16）5x^3-2x^2y+8y-2ax
题目似乎有错，连a都上来了
请查看一下题目好么？谢谢

【希望对你有帮助】

Answer 2

(3-xy)^2
(a+b-9)^2
(2-3m+3n)^2
(x-1)(x^2+x+1)
(1-1/2a)(1+1/2a+1/4a^2)
-a(1+8a^3)
(x+2)(x+5)
(y-3)(y-4)