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\(=x^3-2x^2y+xy^2+5x^2y-10xy^2+5y^3\)
\(=x\left(x^2-2xy+y^2\right)+5y\left(x^2-2xy+y^2\right)\)
\(=\left(x+5y\right)\left(x-y\right)^2\)
\(A=\left(\dfrac{-1}{3}x^5y^2\right).\left(-9xy^3\right)\)
\(A=\left[\left(\dfrac{-1}{3}\right).\left(-9\right)\right].\left(x^5.x\right).\left(y^2.y^3\right)\)
\(A=3x^6y^5\)
\(B=\left(\dfrac{-1}{2}x^2y^3\right).\left(-x^2y^3\right)^3\)
\(B=\left(\dfrac{-1}{2}x^2y^3\right).\left(-x^2\right)^3.\left(y^3\right)^3\)
\(B=\left(\dfrac{-1}{2}x^2y^3\right).\left(-x^6\right).y^9\)
\(B=\left[\left(\dfrac{-1}{2}\right).\left(-1\right)\right].\left(x^2.x^6\right).\left(y^3.y^9\right)\)
\(B=\dfrac{1}{2}x^8y^{12}\)
\(P=3x^2-xy-10xy+15y^2+11xy=3x^2+15y^2\)
Nhan xet: \(3x^2\ge0;15y^2\ge0\)
=> \(3x^2+15y^2\ge0\) => \(P\ge0\)
GTNN cua P la 0 khi x=y=0
$P=3x^2-xy-10xy+15y^2+11xy=3x^2+15y^2$
Nhan xet: $3x^2\ge0;15y^2\ge0$
=> $3x^2+15y^2\ge0$ => $P\ge0$GTNN cua P la 0 khi x=y=0
x3 + 3x2y - 9xy2 + 5y3
= ( x3 - 3x2y + 3xy2 - y3 ) + ( 6y3 - 12xy2 + 6 x2y )
= ( x - y )3 + 6y ( x - y )2
= ( x - y )2 ( x + 5y )
A=3xy2+4x3-5y2x-3x3-9xy3-9xy2-x3
= (3xy2-9xy2)+(4x3-x3-3x3)-5y2x-9xy3
= -6xy2-5y2x-9xy3
Bậc của đa thức là 3
`@` `\text {Ans}`
`\downarrow`
`x^2 - 8xy + 7y^2`
`= x^2 - xy - 7xy + 7y^2`
`= (x^2 - xy) - (7xy - 7y^2)`
`= x(x - y) - 7y(x - y)`
`= (x - 7y)(x - y)`
___
`x^2 - 9xy + 14y^2`
`= x^2 - 2xy - 7xy + 14y^2`
`= (x^2 - 2xy) - (7xy - 14y^2)`
`= x(x - 2y) - 7y(x - 2y)`
`= (x - 7y)(x - 2y)`
___
`x^2 - 11xy + 18y^2`
`= x^2 - 2xy - 9xy + 18y^2`
`= (x^2 - 2xy) - (9xy - 18y^2)`
`= x(x - 2y) - 9y(x - 2y)`
`= (x - 9y)(x - 2y)`
a: =x^2-xy-7xy+7y^2
=x(x-y)-7y(x-y)
=(x-y)(x-7y)
b: =x^2-2xy-7xy+14y^2
=x(x-2y)-7y(x-2y)
=(x-2y)(x-7y)
c: =x^2-2xy-9xy+18y^2
=x(x-2y)-9y(x-2y)
=(x-2y)(x-9y)
11xy-5y+9xy+5y=0
20xy=0
xy=0
x=0;y=0