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x2 - 5x + 5y - y2 =
= -5 (x-y) + (x2 - y2 )
= -5 (x-y) + (x-y)(x+y)
= (x-y) (-5 +x+y)
x2-5x+5y-y2
=x2-y2-5x+5y
=(x2-y2)-5(x+y)
=(x2-y2)(-5+x+y)
\(x^2-y^2-5x+5y=\left(x^2-y^2\right)-\left(5x-5y\right)\)
\(=\left(x+y\right)\left(x-y\right)-5\cdot\left(x-y\right)\)
\(=\left(x-y\right)\cdot\left[\left(x+y\right)-5\right]=\left(x-y\right)\cdot\left(x+y-5\right)\)
a,\(\frac{1}{5}x^2y\left(15xy^2-5y+3xy\right)=3x^3y^3-x^2y^2+\frac{3}{5}x^3y^2\)
b,\(5x^3-5x=5x\left(x^2-1\right)=5x\left(x-1\right)\left(x+1\right)\)
c, \(3x^2+5y-3xy-5x=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(3x-5\right)\left(x-y\right)\)
1) 1/5x2y( 15xy2 - 5y + 3xy ) = 3x3y3 - x2y2 + 3/5x3y2
2) a) 5x3 - 5x = 5x( x2 - 1 ) = 5x( x2 - 12 ) = 5x( x - 1 )( x + 1 )
b) 3x2 + 5y - 3xy - 5x = ( 3x2 - 3xy ) + ( 5y - 5x )
= 3x( x - y ) + 5( y - x )
= 3x( x - y ) + 5[ -( x - y ) ]
= 3x( x - y ) - 5( x - y )
= ( 3x - 5 )( x - y )
a)\(x^2-y^2-x-y=\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-1\right)\)
b)\(x^2-5x+5y-y^2=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-5\right)\)
a) (x-y)(x+y)-(x+y)=(x+y)(x-y-1) b) (x^2-y^2)-(5x-5y)=(x-y)(x+y)-5(x+y)=(x+y)(x-y-5) c) (x^3+1)-3x(x+1)=(x+1)(x^2-x+1)-3x(x+1)=(x+1)(x^2-4x+1)
4(x2+xy+xy+y2)+5x+=5y+1
=4(x2+xy+xy+y2)+4x+4y+x+y+1
=4(x2+xy+xy+y2+x+y)+(x+y+1)
=4(x+y)(x+y+1)+(x+y+1)
=(x+y+1)(4x+4y+1)
Hok tốt
\(4\left(x^2+2xy+y^2\right)+5x+5y+1\)
\(\Rightarrow4\left(x+y\right)^2+5\left(x+y\right)+1\)
\(\Rightarrow\left(x+y\right)\left[4\left(x+y\right)+5+1\right]\)
\(\Rightarrow\left(x+y\right)\left(4\left(x+y\right)+6\right)\)
\(\Rightarrow2\left(x+y\right)\left(2\left(x+y\right)+3\right)\)
Phân tích các đa thức sau thành nhân tử :
a) x - y + 5x - 5y
= ( x + 5x ) - ( y + 5y )
= x . ( 1 + 6 ) - y . ( 1 + 6 )
= ( 1 + 6 ) . ( x - y )
\(a,x-y+5x-5y=\left(x-y\right)+5\left(x-y\right)=6\left(x-y\right)\)
\(5x^2+3\left(x+y\right)^2-5y^2\)
\(=5x^2-5y^2+3\left(x+y\right)^2\)
\(=5\left(x^2-y^2\right)+3\left(x+y\right)^2\)
\(=5\left(x+y\right)\left(x-y\right)+3\left(x+y\right)^2\)
\(=\left(x+y\right)\left[5\left(x-y\right)+3\left(x+y\right)\right]\)
\(=\left(x+y\right)\left[5x-5y+3x+3y\right]\)
\(=\left(x+y\right)\left(8x-2y\right)\)
\(=2\left(x+y\right)\left(4x-y\right)\)