Phan tích thanh nhan tử
\(x^3-4x^2+12x-27\)
\(x^2+y^2-x^2y^2+xy-x-y\)
\(x^7+x^2+1\)
K
Khách
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Những câu hỏi liên quan
AN
28 tháng 9 2017
phan tich cac da thuc sau thanh nhan tu theo mau:
a)\(2x^3-x\)
\(=x\left(2x^2-1\right)\)
\(=x\left(\left(\sqrt{2}x\right)^2-1^2\right)\)\
\(=x\left(\sqrt{2}x-1\right)\left(\sqrt{2}x+1\right)\)
b)\(5x^2\left(x-1\right)-15x\left(x-1\right)\)
\(=\left(5x^2-15x\right)\left(x-1\right)\)
\(=5x\left(x-3\right)\left(x-1\right)\)
d)\(3x\left(x-2y\right)+6y\left(2y-x\right)\)
\(=3x\left(x-2y\right)-6y\left(x-2y\right)\)
\(=\left(3x-6y\right)\left(x-2y\right)\)
\(=3\left(x-2y\right)\left(x-2y\right)\)
\(=3\left(x-2y\right)^2\)
TN
1
TM
27 tháng 9 2017
\(x^2+y^2-x^2y^2+xy-x-y\)\(=\left(xy-x\right)+\left(y^2-y\right)-\left(x^2y^2-x^2\right)\)
\(=x\left(y-1\right)+y\left(y-1\right)-x^2\left(y^2-1\right)\)\(=\left(y-1\right)\left[x+y-x^2\left(y+1\right)\right]\)
\(=\left(y-1\right)\left(x+y-x^2y-x^2\right)\)\(=\left(y-1\right)\left[x\left(1-x\right)+y\left(1-x^2\right)\right]\)
\(=\left(y-1\right)\left(1-x\right)\left[x+y\left(1+x\right)\right]=\left(y-1\right)\left(1-x\right)\left(xy+x+y\right)\)
L
0
22 tháng 5 2022
1: =z(x-y)-5(x-y)=(x-y)(z-5)
2: \(=x^2\left(1-x\right)-xy\left(1-x\right)\)
\(=x\left(1-x\right)\left(x-y\right)\)
3: \(=4x^2-\left(t^2+4ty+4y^2\right)\)
\(=\left(2x\right)^2-\left(t+2y\right)^2\)
\(=\left(2x-t-2y\right)\left(2x+t+2y\right)\)
4: \(=-\left(x^2-4x+4-y^2\right)\)
\(=-\left(x-2-y\right)\left(x-2+y\right)\)
N
23 tháng 7 2017
a) x2 ( x - 3 ) + 12 - 4x = x2 ( x - 3 ) + 4(3 - x) = x2 ( x - 3 ) - 4(x - 3) = (x - 3) (x2 -4) = (x-3) (x-2 ) (x+2)
b) x2 - 4 + (x+2)2 = (x- 2) (x+2) + (x+2)2 = (x+2)(x -2 + x + 2) = 2x(x+ 2)
c) x3 - 2x2 + x - xy2 = x( x2 - 2x + 1 - y2) = x [ (x-1)2 - y2 ] = x(x- 1- y) (x-1 + y)
d) x3 - 4x2 - 12x + 27 = x3 + 3x2 - 7x2 -21x + 9x + 27
= (x3 + 3x2) - (7x2 + 21x) + (9x + 27)
= x2(x + 3) - 7x(x + 3) + 9(x + 3)
= (x + 3)(x2 - 7x + 9)
3 tháng 10 2018
a) x2-x-y2-y=(x2-y2)-(x+y)=(x+y)(x-y)-(x+y)=(x+y)(x-y-1)
b)x2-2xy+y2-z2=(x-y)2-z2=(x-y-z)(x-y+z)
c)5x-5y+ax-ay=5(x-y)+a(x-y)=(x-y)(5+a)
d)a3-a2x-ay+xy=a2(a-x)-y(a-x)=(a-x)(a2-y)
e)4x2-y2+4x+1=[(2x)2+2.2x.1+12]-y2=(2x+1)2-y2=(2x+1-y)(2x+1+y)
Chúc bạn học tốt!
8 tháng 12 2023
2: \(8xy-24xy+16x\)
\(=8x\cdot y-8x\cdot3y+8x\cdot2\)
\(=8x\left(y-3y+2\right)=8x\left(-2y+2\right)\)
\(=-16y\left(y-1\right)\)
3: \(xy-x=x\cdot y-x\cdot1=x\left(y-1\right)\)
11: \(2mx-4m2xy+6mx\)
\(=2mx-2my\cdot4y+2mx\cdot3\)
\(=2mx\left(1-4y+3\right)\)
\(=2mx\left(4-4y\right)=8mx\left(1-y\right)\)
12: \(7x^2y^5-14x^3y^4-21y^3\)
\(=7y^3\cdot x^2y^2-7y^3\cdot2x^3y-7y^3\cdot3\)
\(=7y^3\left(x^2y^2-2x^3y-3\right)\)
13: \(2\left(x-y\right)-a\left(x-y\right)\)
\(=2\cdot\left(x-y\right)-a\cdot\left(x-y\right)\)
\(=\left(x-y\right)\left(2-a\right)\)
x3-4x2+12x-27
=(x3-27)+(-4x2+12x)
=(x-3)(x2+3x+9)-4x.(x-3)
=(x-3)(x2+3x+9-4x)
=(x-3)(x2-x+9)
x2+y2-x2y2+xy-x-y
=x2-x+y2-x2y2+xy-y
=x.(x-1)-y2.(x2-1)+y.(x-1)
=x.(x-1)-y2.(x-1)(x+1)+y.(x-1)
=(x-1)[x-y2.(x+1)+y]
=(x-1)(x-xy2-y2+y)
=(x-1)[-x.(y2-1)-y.(y-1)]
=(x-1)[-x.(y-1)(y+1)-y.(y-1)]
=(x-1)(y-1)[-x.(y+1)-y]
=(x-1)(y-1)(-xy-x-y)