问几个初中的分解因式题!

来源:百度知道 编辑:UC知道 时间:2024/05/31 08:10:34
a^2b^2=0.01 , x^2y-2xy^2+y^3 , 16-(2a+3b)^2 , (a^2+4)^2-16a^2 , a^2x^2+16ax+64 , 9+6(a+b)+(a+b)^2

a^2b^2=0.01 ab=0.1
x^2y-2xy^2+y^3 =y(x-y)^2
16-(2a+3b)^2 =(4+2a+3b)(4-2a-3b)
(a^2+4)^2-16a^2 =(a+2)²(a-2)²
a^2x^2+16ax+64 =(ax+8)²
9+6(a+b)+(a+b)^2 =(3+a+b)²

1.
a^2b^2=0.01
(ab)^2=(0.1)^2
ab=0.1

2.
x^2y-2xy^2+y^3
=y(x^2-2xy+y^2)
=y(x-y)^2

3.
16-(2a+3b)^2
=-[(2a+3b)^2-16]
=-[(2a+3b)-4][(2a+3b)+4]
=-(2a+3b-4)(2a+3b+4)

4.
(a^2+4)^2-16a^2
=(a^2+4)^2-(4a)^2
=[(a^2+4)-(4a)][(a^2+4)+(4a)]
=(a^2+4-4a)(a^2+4+4a)
=(a-2)^2(a+2)^2

5.
a^2x^2+16ax+64
=(ax)^2+16ax+64
=(ax+8)^2

6.
9+6(a+b)+(a+b)^2
=[(a+b)+3]^2
=(a+b+3)^2

分解因式有点复杂~!要详细步骤吗?
第一个那个等号应该是+号吧.
1.a^2b^2+0.01=(a+b)^2+(0.1)^2=(a+b)^2+0.2ab+(0.1)^2-0.2ab=(ab+0.1)^2
-0.2ab如果是=号就是ab=0.1
2.X^2Y-2XY^2+Y^3=Y(X^2-2XY+Y^2)=Y(X-Y)^2
3.16-(2a+3b)^2=4^2-(2a+3b)^2=(4-2a-3b)(4+2a+3b)
4.(a^2+4)^2