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\(giải:\)
\(16x^2y-4xy^2-4x^3+x^2y\)
\(=\left(16x^2y-4xy^2\right)-\left(4x^3-x^2y\right)\)
\(=4xy\left(4x-y\right)-x^2\left(4x-y\right)\)
\(=\left(4x-y\right)\left(4xy-x^2\right)\)
\(=\left(4x-y\right)\left(\sqrt{4xy}-x\right)\left(\sqrt{4xy}+x\right)\)
\(=\left(4x-y\right)\left(2\sqrt{xy}-x\right)\left(2\sqrt{xy}+x\right)\)
Bài làm:
a) \(2x^2+7x+5=\left(2x^2+2x\right)+\left(5x+5\right)=2x\left(x+1\right)+5\left(x+1\right)\)
\(=\left(2x+5\right)\left(x+1\right)\)
b) \(x^3-2x-4=\left(x^3-2x^2\right)+\left(2x^2-4x\right)+\left(2x-4\right)\)
\(=x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)=\left(x-2\right)\left(x^2+2x+2\right)\)
c) \(x^2+4x+3=\left(x^2+x\right)+\left(3x+3\right)=x\left(x+1\right)+3\left(x+1\right)\)
\(=\left(x+1\right)\left(x+3\right)\)
2x2 + 7x + 5 = 2x2 + 2x + 5x + 5 = ( 2x2 + 2x ) + ( 5x + 5 ) = 2x( x + 1 ) + 5( x + 1 ) = ( 2x + 5 )( x + 1 )
x2 + 4x + 3 = x2 + x + 3x + 3 = ( x2 + x ) + ( 3x + 3 ) = x( x + 1 ) + 3( x + 1 ) = ( x + 3 )( x + 1 )
\(3x^3y-6x^2y-3xy^3-6xy^2z-3xyz^2+3xy\)
\(=3xy\left(x^2-2x-y^2-2yz-z^2+1\right)\)
\(=3xy\left[\left(x-1\right)^2-\left(y+z\right)^2\right]\)
\(=3xy\left(x-1-y-z\right)\left(x-1+y+z\right)\)
8x2+30x+7
=8x2+2x+28x+7
=(8x2+2x)+(28x+7)
=2x(4x+1)+7(4x+1)
=(2x+7)(4x+1)