12(16a^2+9b^2+12ab)(1/3a-1/4b)

(a+b）^2-16a^2=a^2+2ab+b^2-16a^2=b^2+2ab-15a^2=(b+5a)(b-3a)
(x^2+4)^2-4x^2=(x^2+4)^2-(2x)^2=(x^2+2x+4)(x^2-2x+4)
m^4-2m^2n^2+n^4=(m^2-n^2)^2=(m+n)^2(m-n)^2
第4题是不是打错了,后一个括号里应该是减号吧：
(x^2-x)^2+1/2（x^2-x)+1/16=(x^2-x+1/4)^2=(x-1/2)^4
4m^2-n^2-6n-9=(2m)^2-(n^2+6n+9)=(2m)^2-(n+3)^2=(2m+n+3)(2m-n-3)
2a-4b+a^2-4b^2=(a^2+2a)-(4b^2+4b)=(a^2+2a+1)-(4b^2+4b+1)
=(a+1)^2-(2b+1)^2=(a+1+2b+1)(a+1-2b-1)=(a+2b+2)(a-2b)
(3a+b)^2-12ab=9a^2+6ab+b^2-12ab=9a^2-6ab+b^2=(3a-b)^2
(m-1)(m-3)+1=m^2-4m+3+1=m^2-4m+4=(m-2)^2
x^2(x^2-2)+1=x^4-2x^2+1=(x^2-1)^2=(x+1)^2(x-1)^2
-x^2-12xy-20y^2=-(x^2+12xy+20y^2)=-(x+2y)(x+10y)
3x^2-11xy+10y^2=(x-2y)(3x-5y)
第12题好象也打错了,第一个括号应该有个2次方的吧：
2(a-1)^2-11(a-1)+12=(a-1-4)[2(a-1)-3]=(a-5)(2a-5)
9a^4-7a^2+1=(9a^4-6a^2+1)-a^2=(3a^2-1)^2-a^2=(3a^2+a-1)(3a^2-a-1)
a^4+a^2b^2+b^4=(a^4+2a^2b^2+b^4)-a^2b^2=(a^2+b^2)^2-(ab)^2
=(a+ab+b)(a-ab+b)

3(a+b)+2(a-b)=3a+3b+2a-2b=5a+b 这是普通加减法
a^2(x-y)-b^2(x-y)=(x-y)(a^2-b2) 这是提取公因式,因为a^2(x-y)和b^2(x-y)都有公因式（x-y)提取出来之后,其余因式做减法运算

(16A^2)^3•(1/8)^4=9
(2^4A^2)^3*(2^(-3))^4=3^2
2^12A^6*2^(-12)=3^2
A^6=3^2
平方
A^12=3^4=81

(1)(a^2+4)^2-16a^2
=(a²+4+4a)(a²+4-4a)
=(a+2)²(a-2)²
(2)(x+y)^2-14(x+y)+49
=(x+y-7)²
(3)a^2b^2-0.01
=(ab+0.1)(ab-0.1)
(4)x^2y-2xy^2+y^3
=y(x²-2xy+y²)
=y(x-y)²
(5)x^2-xy+1/4y^2
=(x-y/2)²
(6)16-(2a+3b)^2
=(4+2a+3b)(4-2a-3b)
(7)a^2 x^2+16ax+64
=(ax+8)²
（8）a^4-8a^2b^2+16b^4
=(a²-4b²)²
=(a+2b)²(a-2b)²
(9)9+6(a+b)^2
此题不能分解
(10)

问下哈,我想知道你式子是2倍根号下（16a²-a）+2-8a嘛?如果是的话可以求导,不知道你高一有学到求导嘛?如果没学到也没关系,以后会知道的,求导之后,令导数等于0,解出来发现导数等于1恒大于0,所以该函数在定义域上单调增,所以当a=1/16时取到极小值也是最小值

4(a-2b)^2-16a^2
=[2(a-2b)-4a][2(a-2b)+4a]
=(-2a-4b)(6a-4b)
=-4(a+2b)(3a-2b)
=4(a+2b)(2b-3a)

4a+1