Question

几道因式分解题求解，好的，正确的重重加分！！！！！！急急急~~~~~~~~~~！！！！！！！！~~~~~~~~

1-16a^2
m^2-9n^2
0.25x^2-81y^2
9a^2x^2-b^2y^2
(x+5)^2-4
(a+b)^2-a^2
49(a-b)^2-16(a+b)^2
(a^2+b^2)^2-a^2b^2
a^2b^2-2ab+1
9-12a+4a^2
x^2+x+1/4
1/4x^2+xy+y^2
(a+b)^2+6(a+b)+9
16-24(x-y)+9(x-y)^2
a^2-2a(b+c)+(b+c)^2
4x^2-4x(y-1)+(y-1)^2
-a+2a^2-a^3
3ax^2-3ay^2
16a^2b_16a^3-4ab^2
a^4-1
x^4-18x^2+81
x^4y^4-8x^2y^2=16

Answer 1

这些因式分解题目都很容易，采用的公式主要是：
1、a^2-b^2=(a+b)(a-b)
2、a^2-2ab+b^2=(a-b)^2
注意分解到底。
因式分解：1、先提取公因式；2、看能否采用公式；3、分组、叉乘。

1-16a^2=(1+4a)(1-4a)
m^2-9n^2=(m+3n)(m-3n)
0.25x^2-81y^2=(0.5x+9y)(0.5x-9y)
9a^2x^2-b^2y^2=(3ax+by)(3ax-by)
(x+5)^2-4=(x+5+2)(x+5-2)=(x+7)(x+3)
(a+b)^2-a^2=(a+b+a)(a+b-a)=b(2a+b)
49(a-b)^2-16(a+b)^2=[7(a-b)+4(a+b)][7(a-b)-4(a+b)]=(11a-3b)(3a-11b)
(a^2+b^2)^2-a^2b^2=(a^2+b^2+ab)(a^2+b^2-ab)
a^2b^2-2ab+1=(ab-1)^2
9-12a+4a^2=(3-2a)^2=(2a-3)^2
x^2+x+1/4=(x+1/2)^2
1/4x^2+xy+y^2=(1/2x+y)^2
(a+b)^2+6(a+b)+9=[(a+b)+3]^2=(a+b+3)^2
16-24(x-y)+9(x-y)^2=[4-3(x-y)]^2=(4-3x+3y)^2
a^2-2a(b+c)+(b+c)^2=[a-(b+c)]^2=(a-b-c)^2
4x^2-4x(y-1)+(y-1)^2=[2x-(y-1)]^2=(2x-y+1)^2
-a+2a^2-a^3=-a(1-2a+a^2)=-a(a+1)^2
3ax^2-3ay^2=3a(x^2-y^2)=3a(x+y)(x-y)
16a^2b_16a^3-4ab^2=4a(4ab-4a^2-b^2)=-4a(4a^2+b^2-4ab)=-4a(2a-b)^2
a^4-1=(a^2+1)(a^2-1)=(a^2+1)(a+1)(a-1)
x^4-18x^2+81=(x^2-9)^2=(x+3)^2(x-3)^2
x^4y^4-8x^2y^2+16=(x^2y^2-4)^2=(xy+2)^2(xy-2)^2（注：原题目有误。）