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6, x mũ 4 - 4x mũ 3 - 8x mũ 2 + 8x =x (x+2) (x^2-6x+4)
8, x mũ 4 + 2x mũ 3 + x mũ 2 - y mũ 2 = -(y-x^2-x) (y+x^2+x)
10, 4x mũ 2 ( x + y ) -x - y = (2x-1) (2x+1) (y+x)
Trả lời:
5, x2 - y2 + 4x + 4
= ( x2 + 4x + 4 ) - y2
= ( x + 2 )2 - y2
= ( x + 2 - y ) ( x + 2 + y )
6, x2 + 2x - 4y2 - 4y
= ( x2 - 4y2 ) + ( 2x - 4y )
= ( x - 2y ) ( x + 2y ) + 2 ( x - 2y )
= ( x - 2y ) ( x + 2y + 2 )
7, 3x2 - 4y + 4x - 3y2
= ( 3x2 - 3y2 ) + ( 4x - 4y )
= 3 ( x2 - y2 ) + 4 ( x - y )
= 3 ( x - y ) ( x + y ) + 4 ( x - y )
= ( x - y ) [ 3 ( x + y ) + 4 ]
= ( x - y ) ( 3x + 3y + 4 )
8, x4 - 6x3 + 54x - 81
= ( x4 - 81 ) - ( 6x3 - 54x )
= ( x2 - 9 ) ( x2 + 9 ) - 6x ( x2 - 9 )
= ( x2 - 9 ) ( x2 + 9 - 6x )
= ( x - 3 ) ( x + 3 ) ( x - 3 )2
= ( x - 3 )3 ( x + 3 )
a, \(x^2-y^2+4x+4=\left(x+2\right)^2-y^2=\left(x+2-y\right)\left(x+2+y\right)\)
b, \(x^2+2x-4y^2-4y=\left(x-2y\right)\left(x+2y\right)+2\left(x-2y\right)=\left(x-2y\right)\left(x+2+2y\right)\)
c, \(3x^2-4y+4x-3y^2=3\left(x-y\right)\left(x+y\right)-4\left(y-x\right)=\left(x-y\right)\left(3x+3y+4\right)\)
d, \(x^4-6x^3+54x-81=\left(x^2+9\right)\left(x-3\right)\left(x+3\right)-6x\left(x^2-9\right)\)
\(=\left(x-3\right)\left(x+3\right)\left(x^2-6x+9\right)=\left(x-3\right)^3\left(x+3\right)\)
\(1,x^2-y^2+4x-4y\)
\(\left(x-y\right)\left(x+y\right)+4\left(x-y\right)\)
\(\left(x-y\right)\left(x+y+4\right)\)
\(x^2+2x-4y^2-4y\)
\(\left(x-2y\right)\left(x+2y\right)+2\left(x-2y\right)\)
\(\left(x-2y\right)\left(x+2y+2\right)\)
\(3,3x^2-4y+4x-3y^2\)
\(3\left(x^2-y^2\right)-4\left(x-y\right)\)
\(3\left(x-y\right)\left(x+y\right)-4\left(x-y\right)\)
\(\left(x-y\right)\left(3x+3y-4\right)\)
\(x^4-6x^3+54x-81\)
\(x^4+3x^3-9x^3+27x^2-27x^2+81x-27x-81\)
\(\left(x^4+3x^3\right)-\left(9x^3+27x^2\right)+\left(27x^2+81x\right)-\left(27x+81\right)\)
\(x^3\left(x+3\right)-9x^2\left(x+3\right)+27x\left(x+3\right)-27\left(x+3\right)\)
\(\left(x+3\right)\left(x^3-9x^2+27x-27\right)\)
\(\left(x+3\right)\left(x-3\right)^3\)
f) = x2( x - 4 ) - 9( x - 4 ) = ( x - 4 )( x - 3 )( x + 3 )
g) = 4( x - y ) + ( x - y )2 = ( x - y )( x - y + 4 )
h) = x3( x + 1 ) + ( x - 1 )( x + 1 ) = ( x + 1 )( x3 + x - 1 )
i) = ( x - y )( x + y ) - 4( x + y ) = ( x + y )( x - y - 4 )
j) = ( x - y )( x2 + xy + y2 ) - 3( x - y ) = ( x - y )( x2 + xy + y2 - 3 )
Trả lời:
f, x3 - 4x2 - 9x + 36 = ( x3 - 4x2 ) - ( 9x - 36 ) = x2 ( x - 4 ) - 9 ( x - 4 ) = ( x - 4 )( x2 - 9 ) = ( x - 4 )( x - 3 )( x + 3 )
g, 4x - 4y + x2 - 2xy + y2 = ( 4x - 4y ) + ( x2 - 2xy + y2 ) = 4 ( x - y ) + ( x - y )2 = ( x - y ) ( 4 + x - y )
h, x4 + x3 + x2 - 1 = ( x4 + x3 ) + ( x2 - 1 ) = x3 ( x + 1 ) + ( x - 1 )( x + 1 ) = ( x + 1 )( x3 + x - 1 )
i, x2 - y2 - 4x - 4y = ( x2 - y2 ) - ( 4x + 4y ) = ( x - y )( x + y ) - 4 ( x + y ) = ( x + y )( x - y - 4 )
j, x3 - y3 - 3x + 3y = ( x3 - y3 ) - ( 3x - 3y ) = ( x - y )( x2 + xy + y2 ) - 3 ( x - y ) = ( x - y )( x2 + xy + y2 - 3 )
\(a,x^2+7x+7y-y^2\)
\(=x^2-y^2+7\left(x+y\right)\)
\(=\left(x-y\right)\left(x+y\right)+7\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y+7\right)\)
\(b,x^2-2x-9y^2+6y\)
\(=x^2-\left(3y\right)^2-2\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x+3y\right)-2\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x+3y-2\right)\)
\(c,x^2-xy+x^3-3x^{2y}+3x^{2y}-y^3\)
\(=x\left(x-y\right)+\left(x-y\right)\left(x^2+xy+y^2\right)\)
\(=\left(x-y\right)\left(x+x^2+xy+y^2\right)\)
