Question

用十字相乘法分解因式

1)a^3-24a^2b+44ab^2
2)6x^2+23xy+20y^2
3)a^6-9a^3+8
4)a^4-21a^2-100
5)a^3-5a^2b-300ab^2
6)(x^2+2)^2-9x^2
7)20x^2-39x+18
8)25x^2y^2-40xy+16
9)a^2-4ab-12b^2
10)x^4+2x^2-3
11)3x^2-11x+10
12)6x^2-11x-10
13)x^2-5x+6

Answer 1

1)a^3-24a^2b+44ab^2
=a(a^2-24ab+44b^2)
=a(a-22b)(a-2b)
2)6x^2+23xy+20y^2
=(2x+5y)(3x+4y)
3)a^6-9a^3+8
=(a^3-8)(a^3-1)
=(a-2)(a^2+4a+4)(a-1)(a^2+a+1)
=(a-2)(a^2+2a+4)(a-1)(a^2+a+1)
4)a^4-21a^2-100
=(a^2-25)(a^2+4)
=(a+5)(a-5)(a^2+4)
5)a^3-5a^2b-300ab^2
=a(a^2- 5ab-300b^2)
=a(a-20b)(a+15b)
6)(x^2+2)^2-9x^2
= (x^2+2+3x)(x^2+2-3x)
= (x+1)(x+2)(x^2+2-3x)
7)20x^2-39x+18
=(4x-3)(5x-6)
8)25x^2y^2-40xy+16
=(5xy-4)^2
9)a^2-4ab-12b^2
=(a-6b)(a+2b)
10)x^4+2x^2-3
=(x^2-1)(x^2+3)
=(x-1)(x+1)(x^2+3)
11)3x^2-11x+10
=(3x-5)(x-2)
12)6x^2-11x-10
=(3x+2)(2x-5)
13)x^2-5x+6
=(x-2)(x-3)

Answer 2

又是你，这么多没有分，我不做。
我不要15分钟可以搞定

追问

我只有5分了

追答

好，我帮你一次
1)a^3-24a^2b+44ab^2 =a(a²-24ab+44b²)=a(a-2b)(a-22b)

2)6x^2+23xy+20y^2 =(2x+5y)(3x+4y)

3)a^6-9a^3+8 =(a³-1)(a³-8)=(a-1)(a-2)(a²+a+1)(a²+2a+4)

4)a^4-21a^2-100 =(a²-25)(a²+4)=(a-5)(a+5)(a²+4)

5)a^3-5a^2b-300ab^2 =a(a²-5ab-300b²)=a(a+15b)(a-20b)

6)(x^2+2)^2-9x^2 =(x²+2-3x)(x²+2+3x)=(x-1)(x-2)(x+1)(x+2)

7)20x^2-39x+18=(2x-2)(10x-9)=2(x-1)(10x-9)

8)25x^2y^2-40xy+16=(5xy-4)²

9)a^2-4ab-12b^2=(a-6b)(a+2b)

10)x^4+2x^2-3 =(x²+3)(x²-1)=(x²+3)(x+1)(x-1)

11)3x^2-11x+10=(3x-5)(x-2)

12)6x^2-11x-10=(2x-5)(3x+2)

13)x^2-5x+6=(x-2)(x-3)

追问

你这是用十字相乘做的么

追答

yes

Answer 3