初二数学题,因式分解 初二数学因式分解题100道

\u521d\u4e8c\u6570\u5b66\u9898\u56e0\u5f0f\u5206\u89e3\u516c\u5f0f\u6cd5

a²+b²=\uff08a-b\uff09²+2ab=25+48=73
\uff08a+b\uff09²=\uff08a-b\uff09²+4ab=121\uff0ca+b=\u6b63\u8d1f11
\u5176\u5b9e\u4e5f\u53ef\u4ee5\u76f4\u63a5\u7b97\u51faa\u548cb\u7684\u503c\u5206\u522b\u662fa=8\uff0cb=3\u6216\u8005 a=-3\uff0cb=-8

1.\u628a\u4e0b\u5217\u5404\u5f0f\u5206\u89e3\u56e0\u5f0f
\uff081\uff0912a3b2\uff0d9a2b+3ab;
\uff082\uff09a\uff08x+y\uff09\uff0d\uff08a\uff0db\uff09\uff08x+y\uff09;
\uff083\uff09121x2\uff0d144y2;
\uff084\uff094\uff08a\uff0db\uff092\uff0d\uff08x\uff0dy\uff092;
\uff085\uff09\uff08x\uff0d2\uff092+10\uff08x\uff0d2\uff09+25;
\uff086\uff09a3\uff08x+y\uff092\uff0d4a3c2.
2.\u7528\u7b80\u4fbf\u65b9\u6cd5\u8ba1\u7b97
\uff081\uff096.42\uff0d3.62;
\uff082\uff0921042\uff0d1042
\uff083\uff091.42\u00d79\uff0d2.32\u00d736



\u7b2c\u4e8c\u7ae0 \u5206\u89e3\u56e0\u5f0f\u7efc\u5408\u7ec3\u4e60
\u4e00\u3001\u9009\u62e9\u9898
1.\u4e0b\u5217\u5404\u5f0f\u4e2d\u4ece\u5de6\u5230\u53f3\u7684\u53d8\u5f62\uff0c\u662f\u56e0\u5f0f\u5206\u89e3\u7684\u662f\uff08 \uff09
(A)(a+3)(a-3)=a2-9 (B)x2+x-5=(x-2)(x+3)+1
(C)a2b+ab2=ab(a+b) (D)x2+1=x(x+ )
2.\u4e0b\u5217\u5404\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3\u4e2d\u6b63\u786e\u7684\u662f\uff08 \uff09
(A)-a2+ab-ac= -a(a+b-c) (B)9xyz-6x2y2=3xyz(3-2xy)
(C)3a2x-6bx+3x=3x(a2-2b) (D) xy2+ x2y= xy(x+y)
3.\u628a\u591a\u9879\u5f0fm2(a-2)+m(2-a)\u5206\u89e3\u56e0\u5f0f\u7b49\u4e8e\uff08 \uff09
(A)(a-2)(m2+m) (B)(a-2)(m2-m) (C)m(a-2)(m-1) (D)m(a-2)(m+1)
4.\u4e0b\u5217\u591a\u9879\u5f0f\u80fd\u5206\u89e3\u56e0\u5f0f\u7684\u662f\uff08 \uff09
(A)x2-y (B)x2+1 (C)x2+y+y2 (D)x2-4x+4
5.\u4e0b\u5217\u591a\u9879\u5f0f\u4e2d\uff0c\u4e0d\u80fd\u7528\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\u5206\u89e3\u56e0\u5f0f\u7684\u662f\uff08 \uff09
(A) (B) (C) (D)
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(A)4x (B)-4x (C)4x4 (D)-4x4
7.\u4e0b\u5217\u5206\u89e3\u56e0\u5f0f\u9519\u8bef\u7684\u662f\uff08 \uff09
(A)15a2+5a=5a(3a+1) (B)-x2-y2= -(x2-y2)= -(x+y)(x-y)
(C)k(x+y)+x+y=(k+1)(x+y) (D)a3-2a2+a=a(a-1)2
8.\u4e0b\u5217\u591a\u9879\u5f0f\u4e2d\u4e0d\u80fd\u7528\u5e73\u65b9\u5dee\u516c\u5f0f\u5206\u89e3\u7684\u662f\uff08 \uff09
(A)-a2+b2 (B)-x2-y2 (C)49x2y2-z2 (D)16m4-25n2p2
9.\u4e0b\u5217\u591a\u9879\u5f0f\uff1a\u246016x5-x\uff1b\u2461(x-1)2-4(x-1)+4\uff1b\u2462(x+1)4-4x(x+1)+4x2\uff1b\u2463-4x2-1+4x\uff0c\u5206\u89e3\u56e0\u5f0f\u540e\uff0c\u7ed3\u679c\u542b\u6709\u76f8\u540c\u56e0\u5f0f\u7684\u662f\uff08 \uff09
(A)\u2460\u2461 (B)\u2461\u2463 (C)\u2462\u2463 (D)\u2461\u2462
10.\u4e24\u4e2a\u8fde\u7eed\u7684\u5947\u6570\u7684\u5e73\u65b9\u5dee\u603b\u53ef\u4ee5\u88ab k\u6574\u9664\uff0c\u5219k\u7b49\u4e8e\uff08 \uff09
(A)4 (B)8 (C)4\u6216-4 (D)8\u7684\u500d\u6570
\u4e8c\u3001\u586b\u7a7a\u9898
11.\u5206\u89e3\u56e0\u5f0f\uff1am3-4m= .
12.\u5df2\u77e5x+y=6\uff0cxy=4\uff0c\u5219x2y+xy2\u7684\u503c\u4e3a .
13.\u5c06xn-yn\u5206\u89e3\u56e0\u5f0f\u7684\u7ed3\u679c\u4e3a(x2+y2)(x+y)(x-y)\uff0c\u5219n\u7684\u503c\u4e3a .
14.\u82e5ax2+24x+b=(mx-3)2\uff0c\u5219a= \uff0cb= \uff0cm= . (\u7b2c15\u9898\u56fe)
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\u4e09\u3001(\u6bcf\u5c0f\u98986\u5206\uff0c\u517124\u5206)
16.\u5206\u89e3\u56e0\u5f0f\uff1a(1)-4x3+16x2-26x (2) a2(x-2a)2- a(2a-x)3


\uff083\uff0956x3yz+14x2y2z\uff0d21xy2z2 (4)mn(m\uff0dn)\uff0dm(n\uff0dm)





17.\u5206\u89e3\u56e0\u5f0f\uff1a(1) 4xy\u2013(x2-4y2) (2)- (2a-b)2+4(a - b)2





18.\u5206\u89e3\u56e0\u5f0f\uff1a(1)-3ma3+6ma2-12ma (2) a2(x-y)+b2(y-x)





19\u3001\u5206\u89e3\u56e0\u5f0f
\uff081\uff09 \uff1b \uff082\uff09 \uff1b




\uff083\uff09 \uff1b





20.\u5206\u89e3\u56e0\u5f0f\uff1a(1) ax2y2+2axy+2a (2)(x2-6x)2+18(x2-6x)+81 (3) \u20132x2n-4xn




21\uff0e\u5c06\u4e0b\u5217\u5404\u5f0f\u5206\u89e3\u56e0\u5f0f\uff1a
\uff081\uff09 \uff1b \uff082\uff09 \uff1b \uff083\uff09 \uff1b


22\uff0e\u5206\u89e3\u56e0\u5f0f\uff081\uff09 \uff1b \uff082\uff09 \uff1b





23.\u7528\u7b80\u4fbf\u65b9\u6cd5\u8ba1\u7b97\uff1a
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26\uff0e\u5c06\u4e0b\u5217\u5404\u5f0f\u5206\u89e3\u56e0\u5f0f
\uff081\uff09




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(3) (4)





(5)




(6)





(7) (8)





(9) \uff0810\uff09(x2+y2)2-4x2y2







\uff0812\uff09\uff0ex6n+2+2x3n+2+x2 \uff0813\uff09\uff0e9(a+1)2(a-1)2-6(a2-1)(b2-1)+(b+1)2(b-1)2







27.\u5df2\u77e5(4x-2y-1)2+ =0\uff0c\u6c424x2y-4x2y2+xy2\u7684\u503c.






28\uff0e\u5df2\u77e5\uff1aa=10000\uff0cb=9999\uff0c\u6c42a2+b2\uff0d2ab\uff0d6a+6b+9\u7684\u503c\u3002






29\uff0e\u8bc1\u660e58-1\u89e3\u88ab20\u223d30\u4e4b\u95f4\u7684\u4e24\u4e2a\u6574\u6570\u6574\u9664






30.\u5199\u4e00\u4e2a\u591a\u9879\u5f0f\uff0c\u518d\u628a\u5b83\u5206\u89e3\u56e0\u5f0f(\u8981\u6c42\uff1a\u591a\u9879\u5f0f\u542b\u6709\u5b57\u6bcdm\u548cn\uff0c\u7cfb\u6570\u3001\u6b21\u6570\u4e0d\u9650\uff0c\u5e76\u80fd\u5148\u7528\u63d0\u53d6\u516c\u56e0\u5f0f\u6cd5\u518d\u7528\u516c\u5f0f\u6cd5\u5206\u89e3).




31.\u89c2\u5bdf\u4e0b\u5217\u5404\u5f0f\uff1a
12+(1\u00d72)2+22=9=32
22+(2\u00d73)2+32=49=72
32+(3\u00d74)2+42=169=132
\u2026\u2026
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32.\u9605\u8bfb\u4e0b\u5217\u56e0\u5f0f\u5206\u89e3\u7684\u8fc7\u7a0b\uff0c\u518d\u56de\u7b54\u6240\u63d0\u51fa\u7684\u95ee\u9898\uff1a
1+x+x(x+1)+x(x+1)2=(1+x)[1+x+x(x+1)]
=(1+x)2(1+x)
=(1+x)3
(1)\u4e0a\u8ff0\u5206\u89e3\u56e0\u5f0f\u7684\u65b9\u6cd5\u662f \uff0c\u5171\u5e94\u7528\u4e86 \u6b21.
(2)\u82e5\u5206\u89e31+x+x(x+1)+x(x+1)2+\u2026+ x(x+1)2004\uff0c\u5219\u9700\u5e94\u7528\u4e0a\u8ff0\u65b9\u6cd5 \u6b21\uff0c\u7ed3\u679c\u662f .
(3)\u5206\u89e3\u56e0\u5f0f\uff1a1+x+x(x+1)+x(x+1)2+\u2026+ x(x+1)n(n\u4e3a\u6b63\u6574\u6570).






34\uff0e\u82e5a\u3001b\u3001c\u4e3a\u25b3ABC\u7684\u4e09\u8fb9\uff0c\u4e14\u6ee1\u8db3a2+b2+c2\uff0dab\uff0dbc\uff0dca=0\u3002\u63a2\u7d22\u25b3ABC\u7684\u5f62\u72b6\uff0c\u5e76\u8bf4\u660e\u7406\u7531\u3002







35\uff0e\u9605\u8bfb\u4e0b\u5217\u8ba1\u7b97\u8fc7\u7a0b\uff1a
99\u00d799+199=992+2\u00d799+1=\uff0899+1\uff092=100 2=10 4
1\uff0e\u8ba1\u7b97\uff1a
999\u00d7999+1999=____________=_______________=_____________=_____________\uff1b
9999\u00d79999+19999=__________=_______________=______________=_______________\u3002
2\uff0e\u731c\u60f39999999999\u00d79999999999+19999999999\u7b49\u4e8e\u591a\u5c11\uff1f\u5199\u51fa\u8ba1\u7b97\u8fc7\u7a0b\u3002







36.\u6709\u82e5\u5e72\u4e2a\u5927\u5c0f\u76f8\u540c\u7684\u5c0f\u7403\u4e00\u4e2a\u6328\u4e00\u4e2a\u6446\u653e\uff0c\u521a\u597d\u6446\u6210\u4e00\u4e2a\u7b49\u8fb9\u4e09\u89d2\u5f62(\u5982\u56fe1)\uff1b\u5c06\u8fd9\u4e9b\u5c0f\u7403\u6362\u4e00\u79cd\u6446\u6cd5\uff0c\u4ecd\u4e00\u4e2a\u6328\u4e00\u4e2a\u6446\u653e\uff0c\u53c8\u521a\u597d\u6446\u6210\u4e00\u4e2a\u6b63\u65b9\u5f62(\u5982\u56fe2).\u8bd5\u95ee\uff1a\u8fd9\u79cd\u5c0f\u7403\u6700\u5c11\u6709\u591a\u5c11\u4e2a\uff1f





\u56fe1 \u56fe2

解:

=(x^2-1)(x^2-6)

=(x+1)(x-1)(x+√6)(x-√6)(十字相乘法)

=(x^2-9)(x^2+4)

=(x-3)(x+3)(x^2+4)(十字相乘法)

=(4x^2-y^2)(x^2-16y^2)

=(2x-y)(2x+y)(x-4y)(x+4y)(十字相乘法)

=(2a+b)(2a-b)+3(2a-b)

=(2a-b)(2a+b+3)(分组分解法)

=x^4-6x^2+9-4x^2

=x^4-10x^2+9

=(x^2-1)(x^2-9)

=(x+1)(x-1)(x+3)(x-3)(十字相乘法)

 

=[x(x-2)-3][x(x-2)+3]

=(x^2-2x-3)(x^2-2x+3)

=(x-3)(x+1)(x^2-2x+3)(平方差公式逆运用)

=(3x²+2x+1+2x²+3x+3)(3x²+2x+1-2x²-3x-3)

=(5x²+5x+4)(x²-x-2)

=(5x²+5x+4)(x+1)(x-2)(平方差公式逆运用)

=(x^2+x-12)(x^2+x-5)

=(x-3)(x+4)(x^2+x-5)(整体看待十字相乘法)

=(x^2+2x-8)(x^2+2x+1)

=(x+4)(x-2)(x+1)^2(整体看待十字相乘法)

=-7xy(x+2y+7xy)(提取公因式法)

 

(先化简再求值)

解:原式=[(a+1)(a+2)]/[a(a+3)]*[(a+3)/(a+1)]=(a+2)/a-(a+2)/2,①

当a=√3时,原式①=√3/6.

即,值为√3/6.

 

解:所以a-4=0且√b-9=0,

∴ a=4且b=81.

∴ 原式=b^2/a^2=6561/16=410.0625.

即,值为410.0625(或6561/16)

 

 

解:令4x-3=0,

解得x=3/4,

代入4x^2+5x+a=0,

得9/4+15/4+a=0

解得:a=-6。

即,a=-6.

 

解:∵ x-1/x=-3,

∴ x^2-2+1/x^2=9,

∴ x^2+1/x^2=11,

∴ x^4+2+1/x^4=121,

∴ x^4+1/x^4=119.

即,值为119.

 

纯手打啊!!!!! 望采纳!!!!!! TAT【很累的。



【1】x四次方-7x²+6=(x^2-1)(x^2-6)=(x-1)(x+1)(x-√6)(x+√6)
【2】x四次方-5x²-36=(x^2-9)(x^2+4)=(x-3)(x+3)(x^2+4)
【3】4x四次方-65x²y²+16y四次方=(4x^2-y^2)(x^2-16y^2)=(2x-y)(2x+y)(x-4y)(x+4y)
【4】4a²-b²+6a-3b=(2a-b)(2a+b)+3(2a-b)=(2a-b)(2a+b+3)
【5】(x²-3)²-4x²=(x^2-2x-3)(x^2+2x-3)=(x-3)(x+1)(x-1)(x+3)
【6】x²(x-2)²-9=(x^2-2x-3)(x^2-2x+3)=(x-3)(x+1)(x^2-2x+3)
【7】(3x²+2x+1)²-(2x²+3x+3)²=(x^2-x-2)(5x^2+5x+4)=(x-2)(x+1)(5x^2+5x+4)

【1】x四次方-7x²+6=(x²-1)(x²-6)=(x-1)(x+1)(x-√6)(x+√6)
【2】x四次方-5x²-36=(x²+4)(x²-9)=(x-3)(x+3)(x²+4)
【3】4x四次方-65x²y²+16y四次方=(4x²-y²)(x²-16y²)=(2x-y)(2x+y)(x-4y)(x+4y)
【4】4a²-b²+6a-3b=(2a-b)(2a+b)+3(2a-b)=(2a-b)(2a+b+3)
【5】(x²-3)²-4x²=(x²-3-2x)(x²-3+2x)=(x+1)(x-3)(x-1)(x+3)
【6】x²(x-2)²-9=(x(x-2)-3)(x(x-2)+3)=(x²-2x-3)(x²-2x+3)=(x+1)(x-3)(x²-2x+3)
【7】(3x²+2x+1)²(2x²+3x+3)² 不能再分解
【8】(x²+x)²-17(x²+x)+60=(x²+x-5)(x²+x-12)=(x-3)(x+4)(x²+x-5)
【9】(x²+2x)²-7(x²+2x)-8=(x²+2x+1)(x²+2x-8)=(x+1)²(x-2)(x+4)
【10】-7x²y-14xy²+49x²y²=-7xy(x+2y-7xy)
二、先化简再求值
(a²+3a)分之(a²+3a+2)除以(a+3)分之(a+1)-(2)分之(a+2),其中a=根号三。
原式=((a+1)(a+2)/(a(a+3)))*((a+3)/(a+1))-(a+2)/2
=(a+2)/a-(a+2)/2=(a+2)(1/a-1/2)=(a+2)(2-a)/2a
=(4-a²)/2a=(4-3)/(2√3)=√3/6
已知|a-4|+(根号b-9)=0,计算(a²+ab)分之(b²)*(a²-ab)分之(a²-b²)的值。
a-4=0, √b-9=0, 所以 a=4,b=81
原式=b²/(a(a+b))*((a+b)(a-b)/(a(a-b)))
=b²/a²=6561/16 (3^8/2^4=(9/2)^4)
如果4x-3是多项式4x²+5x+a的一个因式,求a的值。
设 4x²+5x+a=(4x-3)(x+b)
4x²+5x+a=4x²+4bx-3x-3b
4b-3=5 且 a=-3b
b=2, a=-6
已知x-x分之1= - 3 ,求x的四次方+x的四次方分之1的值
x-1/x=-3
(x-1/x)²=(-3)², x²-2+1/x²=9, x²+1/x²=11
x^4+1/x^4=x^4+2+1/x^4-2
=(x²+1/x²)²-2
=11²-2
=119

【1】(x的平方-1)(x的平方-6)
【2】(x的平方-9(x的平方+4)
【3】题错了没,是不是4x四次方-16x²y²+16y四次方,如果是,答案为(2x的平方-4y的平方)的平方
【5】(x的平方-3+2x)(xDe平方-3-2x)

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