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KT
1
12 tháng 10 2019
\(a.=x^3+3x^2y+3x^2y+9xy^2+3xy^2+9y^3\)
\(=x^2\left(x+3y\right)+3xy\left(x+3y\right)+3y^2\left(x+3y\right)\)
\(=\left(x+3y\right)\left(x^2+3xy+3y^2\right).\)
\(b.=9x^3+3x^2y+9x^2y+3xy^2+3xy^2+y^3\)
\(=3x^2\left(3x+y\right)+3xy\left(3x+y\right)+y^2\left(3x+y\right)\)
\(=\left(3x^2+3xy+y^2\right)\left(3x+y\right)\).
LC
1 tháng 10 2018
d,
\(a^2+2ab+b^2-ac-bc=\left(a+b\right)^2-c\left(a+b\right)\)
\(=\left(a+b\right)\left(a+b-c\right)\)
Vậy..
LC
1 tháng 10 2018
e
\(x^2-2x-4y^2-4y\)
\(=\left(x^2-2x+1\right)-\left(4y^2+4y+1\right)\)
\(=\left(x-1\right)^2-\left(2y+1\right)^2\)
\(=\left(x-2y-2\right)\left(x+2y\right)\)
20 tháng 8 2021
1, \(x^2-y^2-2x+2y=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)=\left(x+y-2\right)\left(x-y\right)\)
2, \(x^2-25+y^2+2xy=\left(x+y\right)^2-5^2=\left(x+y-5\right)\left(x+y+5\right)\)
3, \(x^2y-x^3-9y+9x=x^2\left(y-x\right)-9\left(y-x\right)=\left(x-3\right)\left(x+3\right)\left(y-x\right)\)
4, \(x^4+2x^3+x^2=x^2\left(x^2+2x+1\right)=x^2\left(x+1\right)^2\)
5, \(x^4+8x=x\left(x^3+8\right)=x\left(x+8\right)\left(x^2-8x+64\right)\)
20 tháng 8 2021
\(1,\)
\(x^2-y^2-2x+2y\)
\(=\left(x^2-y^2\right)-\left(2x-2y\right)\)
\(=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-2\right)\)
\(2,\)
\(x^2-25+y^2+2xy\)
\(=\left(x^2+2xy+y^2\right)-25\)
\(=\left(x+y\right)^2-5^2\)
\(=\left(x+y-5\right)\left(x+y+5\right)\)
\(3,\)
\(x^2y-x^3-9y+9x\)
\(=\left(x^2y-x^3\right)-\left(9y-9x\right)\)
\(=x^2\left(y-x\right)-9\left(y-x\right)\)
\(=\left(x^2-9\right)\left(y-x\right)\)
\(=\left(x-3\right)\left(x+3\right)\left(y-x\right)\)
\(4,\)
\(x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
\(5,\)
\(x^4-8x\)
\(=x\left(x^3-8\right)\)
\(=x\left(x-2\right)\left(x^2+2x+4\right)\)
14 tháng 10 2020
16) 2x + 2y - x2 - xy = ( 2x + 2y ) - ( x2 + xy ) = 2( x + y ) - x( x + y ) = ( x + y )( 2 - x )
17) x2 - 2x - 4y2 - 4y = ( x2 - 4y2 ) - ( 2x + 4y ) = ( x - 2y )( x + 2y ) - 2( x + 2y ) = ( x + 2y )( x - 2y - 2 )
18) x2y - x3 - 9y + 9x = ( x2y - x3 ) - ( 9y - 9x ) = x2( y - x ) - 9( y - x ) = ( y - x )( x2 - 9 ) = ( y - x )( x - 3 )( x + 3 )
19) x2( x - 1 ) + 16( 1 - x ) = x2( x - 1 ) - 16( x - 1 ) = ( x - 1 )( x2 - 16 ) = ( x - 1 )( x - 4 )( x + 4 )
20) 2x2 + 3x - 2xy - 3y = ( 2x2 - 2xy ) + ( 3x - 3y ) = 2x( x - y ) + 3( x - y ) = ( x - y )( 2x + 3 )
A
14 tháng 10 2020
20, \(2x^2+3x-2xy-3y=2x\left(x-y\right)+3\left(x-y\right)=\left(2x+3\right)\left(x-y\right)\)
16, \(2x+2y-x^2-xy=2\left(x+y\right)-x\left(x+y\right)=\left(2-x\right)\left(x+y\right)\)
17, \(x^2-2x-4y^2-4y=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)=\left(x-2y-2\right)\left(x+2y\right)\)
18, \(x^2y-x^3-9y+9x=-x\left(x^2-9\right)+y\left(x^2-9\right)=\left(-x-y\right)\left(x^2-9\right)=\left(y-x\right)\left(x-3\right)\left(x+3\right)\)
19, \(x^2\left(x-1\right)+16\left(1-x\right)=x^2\left(x-1\right)-16\left(x-1\right)=\left(x^2-16\right)\left(x-1\right)=\left(x-4\right)\left(x+4\right)\left(x-1\right)\)
DV
1
6 tháng 10 2016
\(\left(a\right)\left(x^2+x\right)^2+9x^2+9x+14\)
\(\text{ Phân tích thành nhân tử}\)
\(\left(x^2+x+2\right)\left(x^2+x+7\right)\)
\(\left(b\right)x^2+2xy+y^2+2x-2y-3\)
\(\text{ Phân tích thành nhân tử}\)
\(y^2+2xy-3y+x^2+2x-3\)
Xong rùi đấy !
CD
2
21 tháng 7 2018
a,x2-4xy+4y2
=(x-2y2
b,4x4+9y2-12x2y
=(2x2)2+(3y)2-12x2y
(2x2-3y)
12 tháng 8 2020
a) 3( x - y ) - 5x( y - x )
= 3( x - y ) - 5x[ -( x - y ) ]
= 3( x - y ) + 5x( x - y )
= ( 3 + 5x )( x - y )
b) x3 + 2x2y + xy2 - 9x
= x( x2 + 2xy + y2 - 9 )
= x[ ( x + y )2 - 32 ]
= x( x + y - 3 )( x + y + 3 )
c) 14x2y - 21xy2 + 28x2y2
= 7xy( 2x - 3y + 4xy )
F
12 tháng 8 2020
Bài giải
\(a,\text{ }3\left(x-y\right)-5x\left(y-x\right)\)
\(=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(x-y\right)\left(3+5x\right)\)
\(b,\text{ }x^3+2x^2y+xy^2-9x\)
\(=x\left(x^2+2xy+y^2-9\right)\)
\(=x\left[\left(x+y\right)^2-3^2\right]\)
\(=x\left(x+y+3\right)\left(x+y-3\right)\)
\(c,\text{ }14x^2y-21xy^2+28x^2y\)
\(=7xy\left(2x-3y+4x\right)\)
\(=7xy\left(6x-3y\right)\)
(x+3)(x-3)(x-y)
\(x^2y-x^3-9y+9x\)
\(=\left(x^2y-x^3\right)-\left(9y-9x\right)\)
\(=x^2.\left(y-x\right)-9.\left(y-x\right)\)
\(=\left(x^2-9\right).\left(y-x\right)\)
\(=\left(x^2-3^2\right).\left(y-x\right)\)
\(=\left(x-3\right).\left(x+3\right).\left(y-x\right)\)