初一因式分解 难的
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1.\uff08x^2-3)^2+2(x^2-3)(x-3)+(x-3)^2
=(x^2-3+x-3)^2
=(x^2+x-6)^2
=(x+3)^2(x-2)^2
2.(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)+22(x^2+8x)+105+15
=(x^2+8x)+22(x^2+8x)+120
=(x^2+8x+10)(x^2+8x+12)
=(x^2+8x+10)(x+2)(x+6)
3.x^2+y^2+4x+2y+3\u2014\u2014\u9898\u76ee\u662f\u4e0d\u662f\u5199\u9519\u4e86\u5440
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+1)(x-y+3)
4.(a^2+a+1)^2+2(a^2+a+1)(a^2+a-1)+(a^2+a-1)^2
=(a^2+a+1+a^2+a-1)^2
=(2a^2+2a)^2
=[2a(a+1)]^2
=4a^2(a+1)^2
5.(x^2+4)^2-16x^2
=(x^2+4+4x)(x^2+4-4x)
=(x+2)^2(x-2)^2
6.(a+b+c)^2-(a-b-c)^2
=(a+b+c+a-b-c)(a+b+c-a+b+c)
=2a(2b+2c)
=4a(b+c)
7.25(x-y)^2-16(x+y)^2
=[5(x-y)+4(x+y)][5(x-y)-4(x+y)]
=(9x-y)(x-9y)
8.x^4-81x^2y^2
=x^2(x^2-9y^2)
=x^2(x+3y)(x-3y)
9.x^2(x-y)+y^2(y-x)
=(x^2-y^2)(x-y)
=(x+y)(x-y)^2
10.(a-b)(x-y)+(b-a)(x+y)
=(b-a)(-x+y+x+y)
=2y(b-a)
(\u4e58\u6cd5)
11.2(2m-1)^2-3(m+1)(m-1)-2(m-1)^2
=8m^2-8m+2-3m^2+3-2m^2+4m-2
=3m^2-4m+3
12.(2x+y+3t)(2x-y-3t)
=(2x)^2-(y+3t)^2
=4x^2-y^2-6ty-9t^2
13.(3a+1)^2(3a-1)^2
=[(3a+1)(3a-1)]^2
=(9a^2-1)^2
=81a^4-18a^2+1
14.(2x-y)(2x+y)-(3x-y)(4x-y)
=4x^2-y^2-(12x^2-7xy+y^2)
=-8x^2+7xy-2y^2
15.(-4x+2y)(-2y-4x)-(2x+3y)(8x-9y)
=(-4x)^2-(2y)^2-(16x^2+6xy-27y^2)
=16x^2-4y^2-16x^2-6xy+27y^2
=23y^2-6xy
16.(2a+b-c)^2
=(2a)^2+2\u00b72a(b-c)+(b-c)^2
=4a^2+4ab-4ac+b^2-2bc+c^2
=4a^2+b^2+c^2+4ab-4ac-2bc
02、a²+b²+c²+2ab-2ac-2bc
03、3x²-147
04、x³-27
05、3x³+192
06、x⁴+6x²+9
07、7x²-28|x|+28
08、3x²-15
09、x+2+√(x+1)
10、x+½-√(x²+x-2)
01、¼x²-2+4/x²=(½ x - 2/x)²;
02、a²+b²+c²+2ab-2ac-2bc=(a+b-c)²;
03、3x²-147=3(x+7)(x-7);
04、x³-27=(x-3)(x²+3x+9);
05、3x³+192=3(x+4)(x²-4x+16);
06、x⁴+6x²+9=(x²+3)²;
07、7x²-28|x|+28=7(|x|-2)²;
08、3x²-15=3(x+√5)(x-√5)
09、x+2+√(x+1)=[√(x+1) + 1]²
10、x+½-√(x²+x-2)=½[2x+1-2√(x²+x-2)]=½[√(x-1)+√(x+2)]²
俗话说:没有最难,只有更难.
对下面的式子进行因式分解:
7854634047473965559808000 + 5361415210454476261939200 x +
1679833256559907126106880 x^2 + 321310109473454304853632 x^3 +
42074529611692088667024 x^4 + 4007363862391302729744 x^5 +
287775325467641891880 x^6 + 15930666887371904304 x^7 +
688874416712280513 x^8 + 23421045420371313 x^9 +
626564678067900 x^10 + 13123624010796 x^11 + 212719408902 x^12 +
2613884742 x^13 + 23528340 x^14 + 146268 x^15 + 561 x^16 + x^17
绝对超难,
结果是:
(9 + x) (12 + x) (15 + x) (18 + x) (21 + x) (24 + x) (27 + x) (30 +
x) (33 + x) (36 + x) (39 + x) (42 + x) (45 + x) (48 + x) (51 +
x) (54 + x) (57 + x)
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