因式分解和整式乘除

题目

因式分解和整式乘除
1）2X×12x³
2）（a+b)-1
3)121x²-9y²2²
4）x²-12x+16
5）a²b²-6ab+9
6）1/9m²+1-2/3m
7）(x²+y²)²-4x²y²
8)ac²(2b+3c)²-ab²(3c+2b)²
9) (a-b)²-2ab(a-b)
10) (x²-3)²+2(3-x²)+1

答案

1）2X×12x³
=24X^4
2）（a+b)-1
=a+b-1

3)121x²-9y²2²
=121x²-36y²
=(11X)²-(6y)²
=(11X+6y)(11X+6y)
4）x²-12x+16
=x²-8x+4²-4x
=(x-4)²-4x
5）a²b²-6ab+9
=(ab)²-6ab+3²
=(ab-3)²
6）1/9m²+1-2/3m
=1/(3m)² -2/3m +1
=(1/3m - 1)²
7）(x²+y²)²-4x²y²
=(x²+y²)²-(2xy)²
=[(x²+y²)-2xy][(x²+y²)+2xy]
=(x-y)²(x+y)²
8)ac²(2b+3c)²-ab²(3c+2b)²
=2abc²+3ac³-3ab²c-2ab³
=(2abc²-2ab³)+(3ac³-3ab²c)
=2ab(c²-b²)+3ac(c²-b²)
=(c²-b²)(2ab+3ac)
=(c+b)(c-b)(2ab+3ac)
9) (a-b)²-2ab(a-b)
=(a-b)(a-b-2ab)
10) (x²-3)²+2(3-x²)+1
=(x²-3)²-2(x²-3)+1
=[(x²-3)-1]²
=(x²-4)²
=[(x+2)(x-2)]²