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NH
1
NV
Nguyễn Việt Lâm
Giáo viên
5 tháng 8 2021
a.
\(x^3-y^3+2x^2-2y^2\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)+\left(x-y\right)\left(2x+2y\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2+2x+2y\right)\)
b.
\(x^3+1-x^2-x\)
\(=\left(x+1\right)\left(x^2-x+1\right)-x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-2x+1\right)\)
\(=\left(x+1\right)\left(x-1\right)^2\)
NH
1
8 tháng 11 2021
b: \(=2x^2-2x-5x+5\)
\(=\left(x-1\right)\left(2x-5\right)\)
8 tháng 11 2021
\(a,=x\left(x^2-4\right)+ax\left(x-2\right)\\ =x\left(x-2\right)\left(x+2\right)+ax\left(x-2\right)\\ =\left(x-2\right)\left(x^2+2x+ax\right)\\ =x\left(x+a+2\right)\left(x-2\right)\\ b,=2x^2-2x-5x+5\\ =2x\left(x-1\right)-5\left(x-1\right)\\ =\left(2x-5\right)\left(x-1\right)\\ c,=\left(x+3\right)\left(x^2-3x+9\right)+\left(x-3\right)\left(x+3\right)\\ =\left(x+3\right)\left(x^2-2x+6\right)\)
VT
0
TG
18 tháng 7 2021
a) \(x^2-2x-4y^2-4y=\left(x^2-4y^2\right)-\left(2x+4y\right)=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)=\left(x+2y\right)\left(x-2y-2\right)\)
b) \(x^3+2x^2+2x+1=\left(x+1\right)\left(x^2-x+1\right)+2x\left(x+1\right)=\left(x+1\right)\left(x^2-x+1+2x\right)=\left(x+1\right)\left(x^2+x+1\right)\)
c) \(x^3-4x^2+12x-27=x^3-3x^2-x^2+3x+9x-27=x^2\left(x-3\right)-x\left(x-3\right)+9\left(x-3\right)=\left(x-3\right)\left(x^2-x+9\right)\)
d) \(a^6-a^4+2a^3+2a^2=a^2\left(a^4-a^2+2a+2\right)=a^2\left[a^2\left(a-1\right)\left(a+1\right)+2\left(a+1\right)\right]=a^2\left(a+1\right)\left(a^3-a^2+2\right)=a^2\left(a+1\right)\left[a^3+a^2-2a^2+2\right]=a^2\left(a+1\right)\left[a^2\left(a+1\right)-2\left(a-1\right)\left(a+1\right)\right]=a^2\left(a+1\right)^2\left(a^2-2a+2\right)\)
18 tháng 7 2021
a) Ta có: \(x^2-2x-4y^2-4y\)
\(=\left(x^2-4y^2\right)-\left(2x+4y\right)\)
\(=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y-2\right)\)
b) Ta có: \(x^3+2x^2+2x+1\)
\(=\left(x^3+1\right)+2x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)+2x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+x+1\right)\)
18 tháng 7 2021
e) Ta có: \(x^4-2x^3+2x-1\)
\(=\left(x^4-1\right)-2x\left(x^2-1\right)\)
\(=\left(x^2+1\right)\left(x-1\right)\left(x+1\right)-2x\left(x-1\right)\left(x+1\right)\)
\(=\left(x-1\right)\left(x+1\right)\cdot\left(x^2-2x+1\right)\)
\(=\left(x+1\right)\cdot\left(x-1\right)^3\)
h) Ta có: \(3x^2-3y^2-2\left(x-y\right)^2\)
\(=3\left(x^2-y^2\right)-2\left(x-y\right)^2\)
\(=3\left(x-y\right)\left(x+y\right)-2\left(x-y\right)^2\)
\(=\left(x-y\right)\left(3x+3y-2x+2y\right)\)
\(=\left(x-y\right)\left(x+5y\right)\)
18 tháng 7 2021
a) Ta có: \(x^2-y^2-2x-2y\)
\(=\left(x-y\right)\left(x+y\right)-2\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-2\right)\)
b) Ta có: \(x^2\left(x+2y\right)-x-2y\)
\(=\left(x+2y\right)\left(x^2-1\right)\)
\(=\left(x+2y\right)\left(x-1\right)\left(x+1\right)\)
16 tháng 7 2021
a) \(4x^2-6x=2x\left(2x-3\right)\)
b) \(9x^4y^3+3x^2y^4=3x^2y^3\left(x^2+y\right)\)
c) \(x^3-2x^2+5x=x\left(x^2-2x+5\right)\)
2
24 tháng 4 2022
`a) 8x^2 - 8xy - 4x + 4y`
`= 8x ( x - y ) - 4 ( x - y )`
`= ( x - y ) ( 8x - 4 )`
__________________________
`b) x^3 + 10x^2 + 25x - xy^2`
`=x ( x^2 + 10x + 25 ) - xy^2`
`= x ( x + 5 )^2 - xy^2`
`= x [ ( x + 5 )^2 - y^2 ]`
`= x ( x + 5 - y ) ( x + 5 + y )`
________________________________
`c) x^2 + x - 6`
`= x^2 + 3x - 2x - 6`
`= x ( x + 3 ) - 2 ( x + 3 )`
`= ( x + 3 ) ( x - 2 )`
_______________________________
`d) 2x^2 + 4x - 16`
`= 2x^2 - 4x + 8x - 16`
`= 2x ( x - 2 ) + 8 ( x - 2 )`
`= ( x - 2 ) ( 2x + 8 )`
LS
24 tháng 4 2022
a) x2 + xy –x – y = x(x + y) – (x + y) = (x + y)(x -1 ).
b) a2 – b2 + 8a + 16 = (a2 + 8a + 16) – b2 = (a + 4)2 – b2
= (a + 4 – b)(a + 4 + b).
tui chỉ làm dc này thui
x3+2x2+x
= x ( x\(^2\) + 2x + 1 )
= x ( x + 1 )\(^2\)