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a) \(7x^3y-3xyz-21x^2+9z\)
\(=7x^2\left(xy-3\right)-3z\left(xy-3\right)\)
\(=\left(7x^2-3z\right)\left(xy-3\right)\)
b) \(4x^2-2x-y^2-y\)
\(=\left[\left(2x\right)^2-y^2\right]-\left(2x+y\right)\)
\(=\left(2x-y\right)\left(2x+y\right)-\left(2x+y\right)\)
\(=\left(2x+y\right)\left(2x-y-1\right)\)
c) \(9x^2-25y^2-6x+10y\)
\(=\left(3x\right)^2-\left(5y\right)^2-2\left(3x-5y\right)\)
\(=\left(3x-5y\right)\left(3x+5y\right)-2\left(3x-5y\right)\)
\(=\left(3x-5y\right)\left(3x+5y-2\right)\)
d) \(\left(5x-4\right)^2+\left(16-25x^2\right)+\left(5x-4\right)\left(3x+2\right)\)
\(=\left(5x-4\right)\left[\left(5x-4\right)+\left(3x+2\right)\right]+\left(4^2-\left(5x\right)^2\right)\)
\(=\left(5x-4\right)\left(8x-2\right)+\left(4-5x\right)\left(4+5x\right)\)
\(=\left(4-5x\right)\left(2-8x\right)+\left(4-5x\right)\left(4+5x\right)\)
\(=\left(4-5x\right)\left[\left(2-8x\right)+\left(4+5x\right)\right]\)
\(=\left(4-5x\right)\left(6-3x\right)\)
a) Ta có: \(-3x^2\left(2x^2-\frac{1}{3}x+2\right)\)
\(=-6x^4+x^3-6x^2\)
b) Ta có: \(2xy^2\left(x-3y+xy\right)\)
\(=2x^2y^2-6xy^3+2x^2y^3\)
c) Ta có: \(\left(5x^2-4x\right)\left(x-2\right)\)
\(=5x^3-10x^2-4x^2+8x\)
\(=5x^3-14x^2+8x\)
d) Ta có: \(-\left(2-x\right)\left(2x+3\right)\)
\(=\left(x-2\right)\left(2x+3\right)\)
\(=2x^2+3x-4x-6\)
\(=2x^2-x-6\)
e) Ta có: \(\left(3x^3-2x^2+x\right):\left(-2x\right)\)
\(=\frac{-3}{2}x^2+x-\frac{1}{2}\)
f) Ta có: \(\left(15x^2y^2-21x^3y+2x^2y\right):\left(3x^2y\right)\)
\(=5y-7x+\frac{2}{3}\)
g) 
Bài làm
a) 4x2 - 6x
= 2x( 2x - 3 )
b) 9x4y3 + 3x2y4
= 3x2y3( 3x2 + y )
c) x3 - 2x2 + 5x
= x( x2 - 2x + 5 )
d) 3x( x - 1 ) + 5( x - 1 )
= ( x - 1 )( 3x + 5 )
e) 2x2( x + 1 ) + 4( x + 1 )
= ( x + 1 )( 2x2 + 4 )
= ( x + 1 )2( x2 + 2 )
= 2( x + 1 )( x2 + 2 )
f) -3x - 6xy + 9xz
= -( 3x + 6xy - 9xz )
= -3x( 1 + 2y - 3z )
# Học tốt #
a,\(xy+3x-7y-21\)
\(=x\left(y+3\right)-7\left(y+3\right)\)
\(=\left(y+3\right)\left(x-7\right)\)
\(b,2xy-15-6x+5y\)
\(=\left(2xy-6x\right)+\left(-15+5y\right)\)
\(=2x\left(y-3\right)-5\left(3-y\right)\)
\(=2x\left(y-3\right)+5\left(y-3\right)\)
\(=\left(y-3\right)\left(2x+5\right)\)
\(c,2x^2y+2xy^2-2x-2y\)
\(=2\left(x+1\right)\left(xy-1\right)\)
\(d,x^2-\left(a+b\right)x+ab\)
\(=\left(a-x\right)\left(b-x\right)\)
\(e,7x^3y-3xyz-21x^2+9z^2\)
\(=\left(xy-3\right)\left(7x^2-3z\right)\)
\(f,4x+4y-x^2\left(x+y\right)\)
\(=-\left(x-2\right)\left(x+2\right)\left(x+y\right)\)
\(g,y^2+y-x^2+x\)
\(=-\left(x-y-1\right)\left(x+y\right)\)
\(h,4x^2-2x-y^2-y\)
\(=\left(2x-y-1\right)\left(2x+y\right)\)
\(i,9x^2-25y^2-6x+10y\)
\(=\left(2x-y-1\right)\left(2x+y\right)\)
\(j,x\left(x+3\right)-5\left(x-5\right)-5\left(x+3\right)\)
\(=\left(3-4x\right)\left(x-5\right)\)
\(k,\left(5x-4\right)\left(4x-5\right)-\left(x-3\right)\left(x-2\right)-\left(5x-4\right)\left(3x-2\right)\)
\(=2\left(2x-1\right)\left(x-3\right)\)
\(l,\left(5x-4\right)\left(4x-5\right)-\left(x-3\right)\left(x-2\right)-\left(5x-4\right)\left(3x-2\right)\)
\(=-4\left(5x-1\right)\left(x-2\right)\)
\(m,\left(5x-4\right)^2+16-25x^2+\left(5x-4\right)\left(3x+2\right)\)
\(=3\left(x-2\right)\left(5x+4\right)\)