高一数学因式分解? 急!!!

来源:百度知道 编辑:UC知道 时间:2024/09/23 19:25:35
因式分解:1. 4a方-20ab+25b方-36
2.x四次方+64
3.x三次方+5x-6
4.2a方b方-7ab+6
5.2xy-x方-y方+1
6.(a+b)(a-b)+c(2b-c)

1. 4a方-20ab+25b方-36

4a^2 - 20ab + 25b^2 - 36
=(2a - 5b)^2 - 6^2
=(2a - 5b + 6)(2a - 5b - 6)

2.x四次方+64

x^4+64
=x^4+16x^2+64-16x^2
=(x^2+8)-(4x)^2
=(x^2-4x+8)(x^2+4x+8)

3.x三次方+5x-6

x^3+5x-6
=x^3-x+6x-6
=x(x^2 - 1)+6(x-1)
=x(x+1)(x-1)+6(x-1)
=(x-1)[x(x+1)+6]
=(x-1)(x^2+x+6)

4.2a方b方-7ab+6
=(2ab-3)(ab-2)

5.2xy-x方-y方+1

2xy-x^2-y^2+1
=1-(x^2-2xy+y^2)
=1-(x-y)^2
=(1-x+y)(1+x-y)

6.(a+b)(a-b)+c(2b-c)
=a^2-b^2+2bc-c^2
=a^2-(b^2-2bc+c^2)
=a^2-(b-c)^2
=(a-b+c)(a+b-c)

1. 4a^2-20ab+25b^2-36=(2a-5b)^2-36=(2a-5b+6)(2a-5b-6)
2.
3.x^3-5x-6=x^3-x^2+x^2+5x-6=x^2(x-1)+(x+6)(x-1)=(x-1)(x^2+x+6)
4.2a^2b^2-7ab+6=(2ab-3)(ab-2)
5.2xy-x^2-y^2+1=1-(x-y)^2=(1-x+y)(1+x-y)

1、=(2a-5b)^2-36=(2a-5b+6)(2a-5b-6)
2、分解不了的。除非是 x^4-64
3、=(x-1)(x^2+x-6)=(x-1)(x-2)(x+3)
4、=(2ab-3)(ab+2)