初一数学因式分解。
\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
\u4e00
x(x-4)-2(x-4)=0
(x-2)(x-4)=0
\u6240\u4ee5x=2\u6216x=4
xy^2-4x^2-1/16y^4=-(4x^2-xy^2+1/16y^4)=-(2x-1/4y^2)^2
3a(x^2+4)^2-48ax^2=3a[(x^2+4)^2-16x^2]=3a[(x^2+4+4x)(x^2+4-4x)]=3a(x+2)^2*(x-2)^2
(x-2y)^2+10(2y-x)+25=(x-2y)^2-10(x-2y)+25=(x-2y-5)^2
2(a^2+b^2)(a+b)^2-(a^2-b^2)=2(a^2+b^2)(a+b)^2-(a-b)(a+b)
=(a+b)[2(a^2+b^2)(a+b)-(a-b)]
\u8bc1\u660e\uff1aa^2+b^2-2a-4b+8=a^2-2a+1+b^2-4b+4+3=(a-1)^2+(b-2)^2+3>=3>0
a^2+b^2-a-4b+17/4=a^2-a+1/4+b^2-4b+4=(a-1/2)^2+(b-2)^2=0
\u6240\u4ee5\uff1aa\uff1d1/2\uff0cb\uff1d2
a^b-ab=(1/2)^2-1/2*2=1/4-1=-3/4
xy^2-4x^2-1/16y^4=-(2x-1/4*y^2)
3a(x^2+4)^2-48ax^2=3a(x^2+4+4x)(x^2+4-4x)
=3a(x+2)^2(x-2)^2
(x-2y)^2+10(2y-x)+25=(x-2y-5)^2
2(a^2+b^2)(a+b)^2-(a^2-b^2)^2
=(a+b)^2(2a^2+2b^2-a^2+2ab-b^2)
=(a+b)^4
\u56e0\u4e3aa^2+b^2-2a-4b+8=(a-1)^2+(b-2)^2+3
\u56e0\u4e3aa^2+b^2-a-4b+17/4=0
\u6240\u4ee5\uff08a-1/2\uff09^2+(b-2)^2=0
a=1/2 b=2
a^b-ab=(1/2)^2-1=-3/4
(1)=-4X^2+XY^2-1/16Y^4
=-(4X^2-XY^2+1/16Y^4)
=-(2X-1/4Y^2)^2
\u4e8c
(3x-1)^2-(x-3)^2=0
(3x-1+x-3)(3x-1-x+3)=0
(4x-4)(2x+2)=0
(x-1)(x+1)=0
=5(6^2-2*8)
=5(36-16)
=100
2.x²-2xy+y²-9=(x-y)^2-3^2
=(x-y+3)(x-y-3)
3.因为 x-y=1
所以 （x-y）^2=1,
而（x-y）^2＝x^2-2xy+y^2
所以 x^2-2xy+y^2=1
因为 x²+y²=25
所以 -2xy＝－24
所以 xy＝12
1
x+y=6
(x+y)²=6²
x²+y²+2xy=36
x²+y²+16=36
x²+y²=20
5x²+5y²=100
2
x²-2xy+y²-9
=(x-y)²-9
=(x-y+3)(x-y-3)
x-y=1
(x-y)²=1
x²+y²-2xy=1
25-2xy=1
2xy=24
xy=12
1.5(x²+y²）
=5{（x+y）²-2xy}
=5{6²-2*8}
=100
2.(x-y)²-9
=（x-y-3）（x-y+3）
3.{（x-y）²-（x²+y²）}/(-2)
=(1-25)/(-2)
=12
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