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a: 2x^2y-50xy=2xy(x-25)
b: 5x^2-10x=5x(x-2)
c: 5x^3-5x=5x(x^2-1)=5x(x-1)(x+1)
d: \(x^2-xy+x=x\left(x-y+1\right)\)
e: x(x-y)-2(y-x)
=x(x-y)+2(x-y)
=(x-y)(x+2)
f: 4x^2-4xy-8y^2
=4(x^2-xy-2y^2)
=4(x^2-2xy+xy-2y^2)
=4[x(x-2y)+y(x-2y)]
=4(x-2y)(x+y)
f1: x^2ỹ-y^2+y
=(x-y)(x+y)+(x+y)
=(x+y)(x-y+1)
a) Ta có: \(x^2-2xy+y^2-2x+2y\)
\(=\left(x-y\right)^2-2\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y-2\right)\)
b) Ta có: \(x^2-4x+4-x^2y+2xy\)
\(=\left(x-2\right)^2-xy\left(x-2\right)\)
\(=\left(x-2\right)\left(x-2-xy\right)\)
a) Ta có: \(x^2y^2-x^2+6xy-9y^2\)
\(=x^2y^2-\left(x^2-6xy+y^2\right)\)
\(=\left(xy\right)^2-\left(x-3y\right)^2\)
\(=\left(xy-x+3y\right)\left(xy+x-3y\right)\)
b) Ta có: \(9-x^2+2xy-y^2\)
\(=9-\left(x^2-2xy+y^2\right)\)
\(=9-\left(x-y\right)^2\)
\(=\left(9-x+y\right)\left(9+x-y\right)\)
\(x^3+8y^3+2xy^2+x^2y\)
\(=x^3+2x^2y-x^2y-2xy^2+4xy^2+8y^3\)
\(=x^2\left(x+2y\right)-xy\left(x+2y\right)+4y^2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x^2-xy+4y^2\right)\)
\(2x^3y-2xy^3-4xy^2-2xy\)
\(=2xy.\left(x^2-y^2-2y-1\right)\)
\(=2xy.[x^2-\left(y^2+2y+1\right)]\)
\(=2xy.[x^2-\left(y+1\right)^2]\)
\(=2xy.\left(x+y+1\right).\left(x-y-1\right)\)
Vậy chọn đáp án A
a) \(x^4+x^3+2x^2+x+1=\left(x^4+x^3+x^2\right)+\left(x^2+x+1\right)\)
\(=x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)=\left(x^2+x+1\right)\left(x^2+1\right)\)
b) \(4x^2-4x-3=4x^2+2x-6x-3=2x\left(2x+1\right)-3\left(2x+1\right)=\left(2x+1\right)\left(2x+3\right)\)
c) \(4x^4+81=4x^4+36x^2+81-36x^2\)
\(=\left(2x^2+9\right)^2-36x^2=\left(2x^2-6x+9\right)\left(2x^2+6x-9\right)\)
d) \(x^2-6xy-25+9y^2=\left(x-3y\right)^2-25=\left(x-3y-5\right)\left(x-3y+5\right)\)
e) \(x^2-8y^2-2xy=x^2+2xy-4xy-8y^2=x\left(x+2y\right)-4y\left(x+2y\right)=\left(x+2y\right)\left(x-4y\right)\)
\(5x^2-10xy+5y^2-20z^2=5\left(x^2-2xy+y^2-4z^2\right)=5.\left[\left(x-y\right)^2-\left(2z\right)^2\right]=5.\left(x-y-2z\right).\left(x-y+2z\right)\)
\(x^2-z^2+y^2-2xy=\left(x-y\right)^2-z^2=\left(x-y+z\right)\left(x-y-z\right)\)
\(x^2-2xy-4z^2+y^2=\left(x-y\right)^2-4z^2=\left(x-y-2z\right)\left(x-y+2z\right)\)
a) 5x2 - 10xy + 5y2
= 5 (x2 - 2xy + y2)
= 5 (x - y)2
b) x2 - z2 + y2 - 2xy
= (x2 + y2 - 2xy) - z2
= (x2 - 2xy + y2) - z2
= (x - y)2 - z2
= (x - y + z)(x - y - z)
c) x2 - 6xy - 25z2 : hinh nhu de bi sai , ban xem lai giup minh
d) x2 - 2xy - 4z2 + y2
= (x2 - 2xy + y2) - 4z2
= (x - y)2 - (2z)2
= (x - y + 2z)(x - y - 2z)
Chuc ban hoc tot
a) \(x^3+8y^3+4x+8y\)
\(=x^3-2x^2y+4xy^2+4x+2x^2y-4xy^2+8y^3+8y\)
\(=\left(x^3-2x^2y+4xy^2+4x\right)+\left(2x^2y-4x^2y+8y^3+8y\right)\)
\(=x\left(x^2-2xy+4y^2+4\right)+2y\left(x^2-2xy+4y^2+4\right)\)
\(=\left(x^2-2xy+4y^2+4\right)\left(x+2y\right)\)
b) \(x^2+6xy+9y^2+5x+15y\)
\(=\left(x^2+6xy+9y^2\right)+\left(5x+15y\right)\)
\(=\left(x+3y\right)^2+5\left(x+3y\right)\)
\(=\left(x+3y\right)\left(x+3y+5\right)\)
c) \(25-x^2+2xy-y^2\)
\(=25-\left(x^2-2xy+y^2\right)\)
\(=25-\left(x-y\right)^2\)
\(=5^2-\left(x-y\right)^2\)
\(=\left(5+x-y\right)\left(5-x+y\right)\)
`x^3+8y^3 +4x+8y`
`=(x+2y)(x^2 - 2xy + 4y^2 ) +4 (x+2y)`
`= (x+2y) (x^2 -2xy +4y^2 +4)`
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`x^2 +6xy +9y^2 +5x+15y`
`= (x+3y)^2 + 5(x+3y)`
`=(x+3y)( x+3y +5)`
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`25-x^2 +2xy -y^2`
`= 25 - (x^2 -2xy+y^2)`
`=25-(x-y)^2`
`=(5-x+y)(5+x-y)`