Question

初一数学题——因式分解

(a+b）^2-16a^2

(x^2+4)^2-4x^2

m^4-2m^2n^2+n^4

(x^2-x)^2+1/2（x^2\x)+1/16

4m^2-n^2-6n-9

2a-4b+a^2-4b^2

(3a+b)^2-12ab

(m-1)(m-3)+1

x^2(x^2-2)+1

-x^2-12xy-20y^2

3x^2-11xy+10y^2

2(a-1)-11(a-1)+12

9a^4-7a^2+1

a^4+a^2b^2+b^4

求解！越详细越好！！！！~~~拜托了~~各位~~！！
错啦 第4题是 （x^2-x)^2+1/2（x^2-x)+1/16

Answer 1

(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)

Answer 2

(a+b）^2-16a^2
原式=(a+b+4a)(a+b-4a)
=(5a+b)(b-3a)

(x^2+4)^2-4x^2
原式=(x^2+4+2x)(x^2+4-2x)

m^4-2m^2n^2+n^4
原式=(m^2-n^2)^2
=(m+n)^2*(m-n)^2

(x^2-x)^2+1/2（x^2\x)+1/16
没有写错吧...

4m^2-n^2-6n-9
原式=4m^2-(n+3)^2
=(4m+n+3)(4m-n-3)

2a-4b+a^2-4b^2
原式=2(a-2b)+(a+2b)(a-2b)
=(a-2b)(2+a+2b)

(3a+b)^2-12ab
原式=9a^2+b^2-6ab
=(3a-b)^2

(m-1)(m-3)+1
原式=m^2-4m+3+1
=m^2-4m+4
=(m-2)^2

x^2(x^2-2)+1
原式=x^4-2x^2+1
=(x^2-1)^2
=(x+1)^2*(x-1)^2

-x^2-12xy-20y^2
原式=-(x^2+12xy+20y^2)
=-(x+2y)(x+10y)

3x^2-11xy+10y^2
原式=(x-2y)(3x-5y)

2(a-1)-11(a-1)+12
题目错了吧?

9a^4-7a^2+1
题目错了吧?

a^4+a^2b^2+b^4
原式=(a^2+b^2)^2

Answer 3

(a+b）^2-16a^2
=（a+b-4a）(a+b+4a)
=(b-3a)(b+5a)

(x^2+4)^2-4x^2
=(x^2+4-2x)(x^2+4+2x)
=[(x-1)^2+3][(x+1)^2+3]

m^4-2m^2n^2+n^4
=(m^2-n^2)^2
=(m-n)^2(m=n)^2

(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
=4m^2-(n+3)^2
=(2m-n-3)(2m+n+3)

2a-4b+a^2-4b^2
=2(a-2b)+(a-2b)(a+2b)
=(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+10y)(x+2y)

3x^2-11xy+10y^2
=(3x-5y)(x-2y)

2(a-1)^2-11(a-1)+12
=[2(a-1)-3](a-1-4)
=(2a-5)(a-5)

9a^4-7a^2+1
=(9a^4-6a^2+1)-a^2
=(3a^2-1)^2-a^2
=(3a^2-1-a)(3a^2-1+a)

a^4+a^2b^2+b^4
=(a^2+b^2)^2-a^2b^2
=(a^2+b^2-ab)(a^2+b^2+ab)

Answer 4

沫，第十四题错了

Answer 5

wa ,,,,,,,,,,,,,