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a,\(8x^2-8xy+2x=2x\left(4x-8y+1\right)\)
b,\(\left(x^2+2x\right)\left(x^2+4x+3\right)-24=x\left(x+2\right)\left(x+1\right)\left(x+3\right)-24\)
\(=\left(x^2+3x\right)\left(x^2+3x+2\right)-24=\left(t+1\right)\left(t-1\right)-24=t^2-5^2=\left(t+5\right)\left(t-5\right)\)
\(=\left(x^2+3x+6\right)\left(x^2+3x-4\right)\)( đặt t = x2 + 3x + 1 )
a) a4 + a2 - 2
a4 + 2a2 - a2 - 2
a2.( a2 + 2 ) - ( a2 + 2 )
( a2 - 1 ).( a2 + 2 )
( a + 1 ).( a - 1 ).( a2 +2 )
b) x4 + 4x2 - 5
x4 + 5x2 - x2 - 5
x2.( x2 + 5 ) - ( x2 + 5 )
( x2 - 1 ).( x2 + 5 )
( x + 1 ).( x - 1 ).( x2 + 5 )
c) x3 - 19x - 30
x3 + 2x2 - 2x2 + 4x - 15x - 30
x2( x + 2 ) - 2x.( x + 2 ) - 15.( x + 2 )
( x + 2 ).( x2 - 2x - 15 )
d) x3 - 7x - 6
x3 - 3x2 + 3x2 - 9x + 2x - 6
x2.( x - 3 ) + 3x.( x - 3 ) + 2.( x - 3 )
( x - 3 ).( x2 + 3x +2 )
( x - 3 ).( x2 + 2x + x + 2 )
( x - 3 ).( x.( x + 2 ) + ( x + 2 )
( x + 1 ).( x + 2 ).( x - 3 )
e) x3 - 5x2 - 14x
x3 - 7x2 + 2x2 - 14x
x2.( x - 7 ) + 2x.( x - 7 )
( x - 7 ).( x2 + 2x )
x.( x + 2 ).( x - 7 )
x 2 - x+ y2 -y - 2xy - 7
= ( x2 - 2xy + y2 ) - ( x + y ) -7
= ( x + y )2 - ( x + y ) -7
= ( x + y ) [ ( x + y ) -7]
= ( x + y ) ( x + y - 7 )
a) \(3\left(x+4\right)-x^2-4x\)
\(=3\left(x+4\right)-x\left(x+4\right)\)
\(=\left(3-x\right)\left(x+4\right)\)
b) \(x^2-2xy+y^2-z^2\)
\(=\left(x-y\right)^2-z^2\)
\(=\left(x-y-z\right)\left(x-y+z\right)\)