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a) ax2 - 2bxy + 2bx2 - axy
= ( ax2 - axy ) + ( 2bx2 - 2bxy )
= ax( x - y ) + 2bx( x - y )
= ( x - y )( ax + 2bx )
= x( x - y )( a + 2b )
b) x2 + 2x - 4y2 + 8y - 3 < đã sửa >
= ( x2 + 2x + 1 ) - ( 4y2 - 8y + 4 )
= ( x + 1 )2 - ( 2y - 2 )2
= [ ( x + 1 ) - ( 2y - 2 ) ][ ( x + 1 ) + ( 2y - 2 ) ]
= ( x + 1 - 2y + 2 )( x + 1 + 2y - 2 )
= ( x - 2y + 3 )( x + 2y - 1 )
c) x4 + 5x3 + 20x - 16
= x4 + 5x3 + 4x2 - 4x2 + 20x - 16
= ( x4 + 5x3 - 4x2 ) + ( 4x2 + 20x - 16 )
= x2( x2 + 5x - 4 ) + 4( x2 + 5x - 4 )
= ( x2 + 5x - 4 )( x2 + 4 )
=x^3 -8y^3 -2(x-2y)
=(x-2y)(x^2 +2xy +4y^2)- 2(x-2y)
=(x-2y)(x^2+2x +4y^2-2)
k day nhe
x2 - 2xy - 8y2 = ( x2 - 2xy + y2 ) - 9y2 = ( x - y )2 - ( 3y )2 ( x - y - 3y ) ( x - y + 3y )
a) 5x2 - 10x = 5x( x - 2 )
b) x2 - y2 - 2x + 2y = (x2 - y2) - (2x - 2y)
= (x - y ) ( x + y)-2 (x-y)
= ( x - y) ( x + y - 2)
c) 4x2 - 4xy - 8y2 = (4x2 - 4xy + 8y2) - 9y2
= (2x - 9y2) - 3y2
= (2x - y - 3y) (2x - y + 3y)
= (2x - 4y) (2x + 2y)
= 4(x - 2y) (x + y)
a) 5x2 - 10x = 5x( x - 2 )
b) x2 - y2 - 2x + 2y = (x2 - y2) - (2x - 2y)
= (x - y ) ( x + y)-2 (x-y)
= ( x - y) ( x + y - 2)
c) 4x2 - 4xy - 8y2 = (4x2 - 4xy + 8y2) - 9y2
= (2x - 9y2) - 3y2
= (2x - y - 3y) (2x - y + 3y)
= (2x - 4y) (2x + 2y)
= 4(x - 2y) (x + y)
D = x2 - 4x - y2 - 8y - 12
= (x2 - 4x + 4) - (y2 + 8y + 16)
= (x - 2)2 - (y + 4)2
= (x + y + 2)(x - y - 6)
\(D=x^2-4x-y^2-8y-12\)
\(=x^2-4x-y^2-8y+4-16\)
\(=\left(x^2-4x+4\right)-\left(y^2+8y+16\right)\)
\(=\left(x-2\right)^2-\left(y+4\right)^2\)
\(=\left(x-2-y-4\right)\left(x-2+y+4\right)\)
\(=\left(x-y-6\right)\left(x+y+2\right)\)
\(x^3+8y^3\)
\(=x^3+\left(2y\right)^3\)
\(=\left(x+2y\right)\left(x^2-2xy+4y^2\right)\)
Bài này khá đơn giản nhé bạn.
x3+8y3
=x3+(2y)3
=(x+2y).(x2-2xy+4y2)
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