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a) \(x^2-10x+9\)
\(=x^2-9x-x+9\)
\(=x\left(x-9\right)-\left(x-9\right)\)
\(=\left(x-1\right)\left(x-9\right)\)
b) \(3x^2-10xy+3y^2\)
\(=3x^2-9xy-xy+3y^2\)
\(=3x\left(x-3y\right)-y\left(x-3y\right)\)
\(=\left(3x-y\right)\left(x-3y\right)\)
a)\(x^2+4x-4y^2-8y\)
\(=x^2+2xy+4x-2xy-4y^2-8y\)
\(=x\left(x+2y+4\right)-2y\left(x+2y+4\right)\)
\(=\left(x-2y\right)\left(x+2y+4\right)\)
b)sai đề
c)sai đề tiếp
a)x2+4x-4y2-8y=(x2-4y2)+(4x-8y)
=(x+2y(x-2y)+4(x-2y)
=(x-2y)(x+2y+4)
\(a)\) \(x^2-2x-4y^2-4y\)
\(=\)\(\left(x^2-2x+1\right)-\left(4y^2+4y+1\right)\)
\(=\)\(\left(x-1\right)^2-\left(2y+1\right)^2\)
\(=\)\(\left(x-1-2y-1\right)\left(x-1+2y+1\right)\)
\(=\)\(\left(x-2y-2\right)\left(x+2y\right)\)
\(=\)\(2\left(x-y\right)\left(x+2y\right)\)
Chúc bạn học tốt ~
a) Ta có x2 - 2x - 4y2 - 4y
= x2 - 2x + 1 - 4y2 - 4y - 1
= (x - 1)2 - (4y2 + 4y + 1)
= (x - 1)2 - (2y + 1)2
= (x - 1 - 2y - 1)(x - 1 + 2y + 1)
= (x - 2y - 1)(x + 2y)
a) \(=x^2+2xy+y^2-x^2+y^2=2xy+2y^2=2y\left(x+y\right)\)
b) \(=\left(x^2-4y^2\right)-\left(2x+4y\right)=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)=\left(x+2y\right)\left(x-2y-2\right)\)
c) \(=3\left[\left(x^2+2xy+y^2\right)-z^2\right]=3\left[\left(x+y\right)^2-z^2\right]=3\left(x+y+z\right)\left(x+y-z\right)\)
d) \(=\left(2xy+1+2x+y\right)\left(2xy+1-2x-y\right)\)
e) \(=\left(x-3\right)\left(x^2+3x+9\right)-2x\left(x-3\right)=\left(x-3\right)\left(x^2+x+9\right)\)
f) \(=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)=\left(x+5\right)\left(x^2-6x+25\right)\)
a) \(\left(x+y\right)^2-\left(x^2-y^2\right)\)
\(=x^2+2xy+y^2-x^2+y^2\)
\(=2y^2+2xy\)
\(=2y\left(x+y\right)\)
c) \(3x^2+6xy+3y^2-3z^2\)
\(=3\left(x^2+2xy+y^2-x^2\right)\)
\(=3\left[\left(x+y\right)^2-z^2\right]\)
\(=3\left(x+y+z\right)\left(x+y-z\right)\)
d) \(\left(2xy+1\right)^2-\left(2x+y\right)^2\)
\(=\left(2xy+1+2x+y\right)\left(2xy+1-2x-y\right)\)
\(=\left[\left(2xy+2x\right)+\left(y+1\right)\right]\left[\left(2xy-2x\right)-\left(y-1\right)\right]\)
\(=\left[2x\left(y+1\right)+\left(y+1\right)\right]\left[2x\left(y-1\right)-\left(y-1\right)\right]\)
\(=\left(2x+1\right)\left(y+1\right)\left(2x-1\right)\left(y-1\right)\)
\(=\left(4x^2-1\right)\left(y^2-1\right)\)
a) \(x^2-10x+9\)
\(=x^2-x-9x+9\)
\(=x\left(x-1\right)-9\left(x-1\right)\)
\(=\left(x-1\right)\left(x-9\right)\)
b) \(3x^2-10xy+3y^2\)
\(=3x^2-xy-9xy+3y^2\)
\(=x\left(3x-y\right)-3y\left(3x-y\right)\)
\(=\left(x-3y\right)\left(3x-y\right)\)
c) \(2x^2-5x+2\)
\(=2x^2-x-4x+2\)
\(=x\left(2x-1\right)-2\left(2x-1\right)\)
\(=\left(2x-1\right)\left(x-2\right)\)
d) \(2xy-x^2+3y^2-4y+1\)
\(=-\left(x^2-2xy+y^2\right)+\left(4y^2-4y+1\right)\)
\(=-\left(x-y\right)^2+\left(2y-1\right)^2\)
\(=\left(2y-1\right)^2-\left(x-y\right)^2\)
\(=\left(2y-1-x+y\right)\left(2y-1+x-y\right)\)
\(=\left(3y-x-1\right)\left(x+y-1\right)\)
\(a.=-4\left(x^2-2x+1\right)\)
\(=-4\left(x-1\right)^2\)
\(b.=3x\left(x-2\right)+2y\left(x-2\right)\)
\(=\left(3x+2y\right)\left(x-2\right)\)
2xy - x2 - y2 + 36=-(x2-2xy+y2-36)=-(x-y)2-36=-(x-y-6)(x-y+6)
a) x2( 1 - x2 ) - 4 - 4x2
= x2 - x4 - 4 - 4x2
= -x4 - 3x2 - 4
= x2 - ( x4 + 4x2 + 4 )
= x2 - ( x2 + 2 )2
= ( x - x2 - 2 )( x2 + x + 2 )
b) 5x2 - 45y2 - 30y - 5
= 5( x2 - 9y2 - 6y - 1 )
= 5[ x2 - ( 9y2 + 6y + 1 ) ]
= 5[ x2 - ( 3y + 1 )2 ]
= 5( x - 3y - 1 )( x + 3y + 1 )
c) x6 - x4 - 9x3 + 9x2 = x4( x2 - 1 ) - 9x( x2 - 1 ) = ( x2 - 1 )( x4 - 9x ) = x( x - 1 )( x + 1 )( x3 - 9 )
d) 3x - 3y + x2 - y2 = 3( x - y ) + ( x - y )( x + y ) = ( x - y )( 3 + x + y )
e) x2 - 2x - 4y2 - 4y = ( x2 - 2x + 1 ) - ( 4y2 + 4y + 1 ) = ( x - 1 )2 - ( 2y + 1 )2 = ( x - 1 - 2y - 1 )( x - 1 + 2y + 1 ) = ( x - 2y - 2 )( x + 2y )