初一数学因式分解 （高分）
\u521d\u4e00\u6570\u5b66\u56e0\u5f0f\u5206\u89e31.
\uff083x²+2x-8\uff09²-\uff08x²-2x-8\uff09²
=(3x²+2x-8+x²-2x-8)(3x²+2x-8-x²+2x+8)
=(4x²-16)(2x²+4x)
=8(x²-4)(x²+2x)
=8x(x+2)(x-2)(x+2)
=8x(x+2)^2(x-2)
2.
(x+2)(x+3)+x²-4
=x^2+5x+6+x^2-4
=2x^2+5x+2
=(x+2)(2x+1)
3.
x²\uff08a-b)+16(b-a)
=(a-b)(x^2-16)
=(a-b)(x+4)(x-4)
4.
\uff08x²+2x\uff09²-7\uff08x²+2x)-8
=(x^2+2x-8)(x^2+2x+1)
=(x-2)(x+4)(x+1)^2
5.
(x²+9y²\uff09²-36x²y²
=(x²+9y²+6x²y²)(x²+9y²-6x²y²)
=(x+3y)^2(x-3y)^2
6.
\uff08x-1\uff09\uff08x-2y-1)+y²
=x^2-2xy-x-x+2y+1+y²
=x^2-2xy+y²-2x+2y+1
=(x-y)^2-2(x-y)+1
=(x-y-1)^2
1.
(x+1)(x+3)(x+5)(x+7)+15
=[(x+1)(x+7)][(x+3)(x+5)]+15
=(x^2+8x+7)(x^2+8x+15)+15
=(x^2+8x+7)[(x^2+8x+7)+8]+15
=(x^2+8x+7)^2+8(x^2+8x+7)+15
=[(x^2+8x+7)+3][(x^2+8x+7)+5]
=(x^2+8x+10)(x^2+8x+12)
=(x^2+8x+10)(x+2)(x+6)
2.
x^2-2xy+y^2-13x+13y+30
=(x-y)^2-13(x-y)+30
=(x-y-3)(x-y-10)
3:
\u5148\u628a4(x+2z)(x-2z)+12xy+9y^2\u5206\u89e3\u56e0\u5f0f\uff0c\u5728\u6c42\u503c\uff0c\u5176\u4e2dx\uff1d1/2\uff0cy\uff1d2/3\uff0cz\uff1d3/4.
\u539f\u5f0f=4(x^2-4z^2)+12xy+9y^2=(4x^2+12xy+9y^2)-16z^2
=(2x+3y)^2-16z^2
=(2x+3y+4z)(2x+3y-4z)
=(1+2+3)(1+2-3)
=0
4:
\u5df2\u77e5a,b,c\u4e3a\u4e09\u89d2\u5f62ABC\u4e09\u8fb9,\u4e14a,b,c\u6ee1\u8db3(a+b+c)^2=3(a^2+b^2+c^2)\uff0e\u95ee\u4e09\u89d2\u5f62ABC\u662f\u54ea\u79cd\u4e09\u89d2\u5f62\uff1f
(A+B+C)^2=3(A^2+B^2+C^2)
A^2+B^2+C^2+2AB+2AC+2BC=3A^2+3B^2+3C^2
2AB+2AC+2BC=2A^2+2B^2+2C^2
A^2-2AB+B^2+A^2-2AC+C^2+B^2-2BC+C^2=0
(A-B)^2+(A-C)^2+(B-C)^2=0
A-B=0,A-C=0,B-C=0
A=B=C
\u7b49\u8fb9\u4e09\u89d2\u5f62
=(2a+b)[(2a-3b)-8a]
=(2a+b)(-6a-3b)
=-3(2a+b)(2a+b)
=-3(2a+b)^2
2.16(x-y)^2-9(x+y)^2
=[4(x-y)-3(x+y)][4(x-y)+3(x+y)]
=(x-7y)(7x-y)
3.x^4-x^3-x+1
=x^3(x-1)-(x-1)
=(x-1)(x^3-1)
=(x-1)(x-1)(x^2+x+1)
=(x-1)^2(x^2+x+1)
4.4x^4-1
=(2x^2-1)(2x^2+1)
=(√2x-1)(√2x+1)(2x^2+1)
5.(x+y)^2-4(x+y-1)
=(x+y)^2-4(x+y)+4
=(x+y-2)^2
6.x^2-y^2+4x+2y+3
=x^2+4x+4-y^2+2y-1
=(x+2)^2-(y-1)^2
=[(x+2)-(y-1)][(x+2)+(y-1)]
=(x-y+3)(x+y+1)
7.a-a^5
=a(1-a^4)
=a(1-a^2)(1+a^2)
=a(1-a)(1+a)(1+a^2)
8.36(a-b)^2-25(a+b)^2
=[6(a-b)-5(a+b)][6(a-b)+5(a+b)]
=(a-11b)(11a-b)
9.(x+y)^2-10(x+y)+25
=(x+y-5)^2
10.x^4-81x^2y^2
=x^2(x^2-81y^2)
=x^2(x-9y)(x+9y)
11.a^2-4ab+4b^2-9c^2
=(a-2b)^2-9c^2
=(a-2b-3c)(a-2b+3c)
12.9x^2-18x+9-y^2-2y-1
=9(x^2-2x+1)-(y^2+2y+1)
=9(x-1)^2-(y+1)^2
=[3(x-1)-(y+1)][3(x-1)+(y+1)]
=(3x-y-4)(3x+y-2)
量太多了 吧。
1。解：（2a+b）(2a-3b)-8a(2a+b)
=(2a+b)*[(2a-3b)-8a]
=(2a+b)*(2a-3b-8a)
=-3*(2a+b)*(2a+b)
=-3*(2a+b)^2
2. 解：16(x-y)^2-9(x+y)^2
=[4(x-y)]^2-[3(x+y)]^2
=(4x-4y+3x+3y)(4x-4y-3x-3y)
=(7x-y)(x-7y)
3。解：x^4-x^3-x+1
=x^3(x-1)-(x-1)
=(x-1)(x^3-1)
=(x-1)(x-1)(x^2+x+1)
(x-1)^2(x^2+x+1)
4.解：4x^4-1
=[(2x^2)^2-1]
=(2x^2+1)(2x^2-1)
5.解：(x+y)^2-4(x+y-1)
=
1.（2a+b）(2a-3b)-8a(2a+b)=(2a+b）(2a-3b-8a)（提取公因式2a+b）
2.16(x-y)^2-9(x+y)^2=(16-9)(x-y)^2=7(x-y)^2(提取公因式(x+y)^2)
3.x^4-x^3-x+1=(x^3-1)(x-1)(十字相乘法）
4.4x^4-1=（2x^2+1)(2x^2-1)(完全平方差）
明天再回答，我先睡了。
1提取公因式即可：2,4平方差公式求解；3先分组在提取公因式（x-1）;5，(x+y)^2-4(x+y)+4=(x+y-2);6，分组配成平方差公式；7提取a在用两次平方差公式；8，10方差公式求解；9，配成完全平方式，即可求解。11，先配成完全平方式，再运用平方差公式；10，先分组配成完全平方，再用平方差公式即可去解。
ok出点难的，再传。
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