Phân tích các đa thức sau nhân tử pp đặt nhân tử chung 2x+2y-x^2-xy Giúp mềnh v
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\(2ab^2-a^2b-b^3\)
\(=-b\left(a^2-2ab+b^2\right)\)
\(=-b\left(a-b\right)^2\)
16) 2x + 2y - x2 - xy = ( 2x + 2y ) - ( x2 + xy ) = 2( x + y ) - x( x + y ) = ( x + y )( 2 - x )
17) x2 - 2x - 4y2 - 4y = ( x2 - 4y2 ) - ( 2x + 4y ) = ( x - 2y )( x + 2y ) - 2( x + 2y ) = ( x + 2y )( x - 2y - 2 )
18) x2y - x3 - 9y + 9x = ( x2y - x3 ) - ( 9y - 9x ) = x2( y - x ) - 9( y - x ) = ( y - x )( x2 - 9 ) = ( y - x )( x - 3 )( x + 3 )
19) x2( x - 1 ) + 16( 1 - x ) = x2( x - 1 ) - 16( x - 1 ) = ( x - 1 )( x2 - 16 ) = ( x - 1 )( x - 4 )( x + 4 )
20) 2x2 + 3x - 2xy - 3y = ( 2x2 - 2xy ) + ( 3x - 3y ) = 2x( x - y ) + 3( x - y ) = ( x - y )( 2x + 3 )
20, \(2x^2+3x-2xy-3y=2x\left(x-y\right)+3\left(x-y\right)=\left(2x+3\right)\left(x-y\right)\)
16, \(2x+2y-x^2-xy=2\left(x+y\right)-x\left(x+y\right)=\left(2-x\right)\left(x+y\right)\)
17, \(x^2-2x-4y^2-4y=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)=\left(x-2y-2\right)\left(x+2y\right)\)
18, \(x^2y-x^3-9y+9x=-x\left(x^2-9\right)+y\left(x^2-9\right)=\left(-x-y\right)\left(x^2-9\right)=\left(y-x\right)\left(x-3\right)\left(x+3\right)\)
19, \(x^2\left(x-1\right)+16\left(1-x\right)=x^2\left(x-1\right)-16\left(x-1\right)=\left(x^2-16\right)\left(x-1\right)=\left(x-4\right)\left(x+4\right)\left(x-1\right)\)
h) \(y\left(y-x\right)^3-x\left(x-y\right)^2+xy\left(x-y\right)=y\left(y-x\right)^3-x\left(y-x\right)^2-xy\left(y-x\right)=\left(y-x\right)\left[y\left(y-x\right)^2-x-xy\right]=\left(y-x\right)\left[y\left(y^2-2xy+x^2\right)-x-xy\right]=\left(y-x\right)\left(y^3-2xy^2+x^2y-x-xy\right)\)
i) \(10x^2\left(a-2b\right)^2-\left(x^2+2\right)\left(2b-a\right)^2=10x^2\left(a-2b\right)^2-\left(x^2+2\right)\left(a-2b\right)^2=\left(a-2b\right)^2\left(10x^2-x^2-2\right)=\left(a-2b\right)^2\left(9x^2-2\right)\)
8: \(=\left(x-2y\right)\cdot x\cdot\left(x+3\right)\)
9: \(=\left(5x+2\right)\left(x-3\right)-x\left(x-3\right)\)
\(=\left(x-3\right)\left(4x+2\right)\)
=2(2x+1)(x-3)
3: \(=2\left(x+2\right)\left(25x-15-x\right)\)
\(=2\left(x+2\right)\left(24x-15\right)\)
=6(x+2)(8x-5)
a) xy+3x-7y-21
=x(y+3)-7(x+3)
=(x-7)(y+3)
b)2xy-15-6x-5y
=2x(y-3)-5(-3+y)
=(2x-5)(y-3)
c)2x^2y+2xy^2-2x-2y
=2x(xy-1)+2y(xy-1)
=(2x+2y)(xy-1)
x(x+3)-5x(x-5)-5(x+3)
=(x-5)(x+3)-5x(x-5)
=(x-5)(x+3-5x)
Câu cuối mình bị nhầm dòng cuối phải là (x-5)(x+3+x-5)=(x-5)(2x-2)nha bạn
2(x + y) - x(x + y) = (2 - x)(x + y)
\(2x+2y-x^2-xy\)
\(=2\left(x+y\right)-x\left(x+y\right)\)
\(=\left(x+y\right)\left(2-x\right)\)