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7 tháng 9 2018
\(x^3-3x^2-3x+1=\left(x^3+x^2\right)-\left(4x^2+4x\right)+\left(x+1\right)=\left(x+1\right)\left(x^2-4x+1\right)=\left(x+1\right).\left(x-1\right)^2\)
\(x^3-4x^2-4x+1=\left(x^3+x^2\right)-\left(5x^2+5x\right)+\left(x+1\right)=\left(x+1\right)\left(x^2-5x+1\right)\)
\(x^3+x^2-2x-8=\left(x^3-2x^2\right)+\left(3x^2-6x\right)+\left(4x-8\right)=\left(x-2\right)\left(x^2+3x-4\right)\)
\(x^4+2x^3+6x-9=\left(x^4-x^3\right)+\left(3x^3-3x\right)+\left(9x-9\right)=\left(x-1\right)\left[x^3-3x\left(x+1\right)+9\right]\)
Tham khảo nhé~
29 tháng 9 2017
a, (2xy+1)2-(2x+y)2=(2xy+1-2x-y)(2xy+1+x+y)=[(2xy-2x)-(y-1)][(2xy+2x)-(y+1)]=[2x(y-1)-(y-1)][2x(y+1) +(y+1)]
=(y-a)(2x-1)(2x+1)(y+1)
b, x2(x-2)2-(x-2)2-x2+1=[x2(x-2)2-(x-2)2] - (x2-1)=(x-2)2(x2-1) - (x2-1)=(x2-1)[(x-2)2-1]=(x-1)(x+1)(x+1)(x-3)
c,x4+2x3-2x-1=(x4-1)+(2x3-2x)=(x2-1)(x2 +1)+2x(x2-1)=(x2-1)(x2+2x+1)=(x-1)(x+1)(x+1)2
d,1+6x-6x2-x3=
20 tháng 5 2018
a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - 1/8 = (2x)3 – (1/2)3 = (2x - 1/2)[(2x)2 + 2x . 12 + (1/2)2]
= (2x - 1/2)(4x2 + x + 1/4)
d)1/25x2 – 64y2 = (1/5x)2(1/5x)2- (8y)2 = (1/5x + 8y)(1/5x - 8y)
ML
8 tháng 8 2015
a)x4-1=(x2-1)(x2+1)=(x-1)(x+1)(x2+1)
b)x2-y2-2x+2y=(x-y)(x+y)-2(x-y)=(x-y)(x+y-2)
c)x2-6x-y2+9=(x2-6x+9)-y2=(x-3)2-y2=(x-y-3)(x+y-3)
d)5x2+3(x+y)2-5y2
=5(x2-y2)+3(x+y)2
=5(x-y)(x+y)+3(x+y)2
=(x+y)(5x-5y+3x+3y)
=(x+y)(8x-2y)
DH
13 tháng 7 2017
a, \(\left(x+3\right)^3-\left(x+2\right)\left(x-2\right)-6x^2-20\)
\(=x^3+9x^2+27x+27-\left(x^2-4\right)-6x^2-20\)
\(=x^3+9x^2+27x+27-x^2+4+6x^2+20\)
\(=x^3+14x^2+27x+51\)
b, \(\left(2x+3\right)\left(4x^2-6x+9\right)-\left(2x-3\right)\left(4x^2+6x+9\right)\)
\(=8x^3-12x^2+18x+12x^2-18x+18-\left(8x^3+12x^2+18x-12x^2-18x-18\right)\)
\(=8x^3+18-8x^3+18=36\)
c, \(\left(2x-1\right)\left(4x^2+2x+1\right)\left(2x+1\right)\left(4x^2-2x+1\right)\)
\(=\left(8x^3+4x^2+2x-4x^2-2x-1\right)\left(8x^3-4x^2+2x+4x^2-2x+1\right)\)
\(=\left(8x^3-1\right)\left(8x^3+1\right)=\left(8x^3\right)^2-1\)
\(=64x^5-1\)
d, \(\left(x+4\right)\left(x^2-4x+16\right)-\left(50+x^2\right)\)
\(=x^3-4x^2+16x+4x^2-16x+64-50-x^2\)
\(=x^3-x^2+14\)
Chúc bạn học tốt!!!
28 tháng 8 2016
\(x^2+6x-y^2+9\)
\(=\left(x^2+6x+9\right)-y^2\)
\(=\left(x+3\right)^2-y^2\)
\(=\left(x+3-y\right)\left(x+3+y\right)\)
17 tháng 7 2018
a) \(x^2-2x+x\)
\(=x^2-x=x\left(x-1\right)\)
b) \(x^2+y^2-2xy-9\)
\(=\left(x-y\right)^2-3^2\)
\(=\left(x-y-3\right)\left(x-y+3\right)\)
c) \(x^2-y^2+6x+9\)
\(=\left(x^2+6x+9\right)-y^2\)
\(=\left(x+3\right)^2-y^2\)
\(=\left(x+3-y\right)\left(x+3+y\right)\)
17 tháng 7 2018
\(x^2-2x+x\)
\(=\left(x^2-2x.1+1\right)+\left(x-1\right)\)
\(=\left(x-1\right)^2+\left(x-1\right)\)
\(=\left(x-1\right)\left(x-1+1\right)\)
\(=x.\left(x-1\right)\)
TT
10 tháng 8 2020
1) \(x^4+2x^3-9x^2-10x-24\)
\(=x^4+4x^3+x^2-2x^3-8x^2-2x-2x^2-8x-2\)
\(=x^2.\left(x^2+4x+1\right)-2x.\left(x^2+4x+1\right)-2.\left(x^2+4x+1\right)\)
\(=\left(x^2+4x+1\right)\left(x^2-2x-2\right)\)
2) \(6x^4+7x^3+5x^2-x-2\)
\(=6x^4-3x^3+10x^3-5x^2+10x^2-5x+4x-2\)
\(=3x^3\left(2x-1\right)+5x^2\left(2x-1\right)+5x\left(2x-1\right)+2\left(2x-1\right)\)
\(=\left(2x-1\right)\left(3x^3+5x^2+5x+2\right)\)
\(=\left(2x-1\right)\left(3x^2+2x^2+3x^2+2x+3x+2\right)\)
\(=\left(2x-1\right)\left(3x+2\right)\left(x^2+x+1\right)\)
3) \(2x^4+3x^3+2x^2-1\)
\(=2x^4+2x^3+x^3+x^2+x^2+x-x-1\)
\(=\left(x+1\right)\left(2x^3+x^2+x-1\right)\)
\(=\left(x+1\right)\left(2x-1\right)\left(x^2+x+1\right)\)
4) \(x^3-x^2-x-2\)
\(=x^3-2x^2+x^2-2x+x-2\)
\(=\left(x-2\right)\left(x^2+x+1\right)\)
\(x^4+2x^3-6x-9.\)
\(=\left(x^2\right)^2+2.x^2.x+x^2-x^2-2.3.x-3^2\)
\(=\left(x^2+x\right)^2-\left(x^2+2.3.x+3^2\right)\)
\(=\left(x^2+x\right)^2-\left(x+3\right)^2\)
\(=\left[\left(x^2+x\right)+\left(x+3\right)\right].\left[\left(x^2+x\right)-\left(x+3\right)\right]\)
\(=\left(x^2+x+x+3\right).\left(x^2+x-x-3\right)\)
\(=\left(x^2+2x+3\right).\left(x^2-3\right)\)