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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) \(\left(5x-4\right)^2+\left(16-25x^2\right)+\left(5x-4\right)\left(3x+2\right)\)
\(=\left(5x-4\right)\left[\left(5x-4\right)+\left(3x+2\right)\right]+\left(4^2-\left(5x\right)^2\right)\)
\(=\left(5x-4\right)\left(8x-2\right)+\left(4-5x\right)\left(4+5x\right)\)
\(=\left(4-5x\right)\left(2-8x\right)+\left(4-5x\right)\left(4+5x\right)\)
\(=\left(4-5x\right)\left[\left(2-8x\right)+\left(4+5x\right)\right]\)
\(=\left(4-5x\right)\left(6-3x\right)\)
Bài làm
a) 2x2y - 4xy2 + 6xy
= 2xy( x - 2y + 3 )
b) 4x3y2 - 8x2y3 + 2x4y
= 2x2y( 2xy - 4y2 + x2 )
c) 9x2y3 - 3x4y2 - 6x3y2 + 18y4
= 3y2( 3x2y - x4 - 2x3 + 6y2 )
d) 7x2y2 - 21xy2z + 7xyz - 14xy
= 7xy( xy - 3yz + z - 2 )
# Học tốt #
a,\(x^2y^2+y^3+zx^2+yz=\left(x^2y^2+y^3\right)+\left(zx^2+yz\right)\)
\(=y^2\left(x^2+y\right)+z\left(x^2+y\right)\)
\(=\left(y^2+z\right)\left(x^2+y\right)\)
b,\(x^4+2x^3-4x-4=x^4+2x^3+x^2-x^2-4x-4\)
\(=\left(x^4+2x^3+x^2\right)-\left(x^2+4x+4\right)\)
\(=\left(x^2+x\right)^2-\left(x+2\right)^2\)
\(=\left(x^2+x-x-2\right)\left(x^2+x+x+2\right)\)
\(=\left(x^2-2\right)\left(x^2+2x+2\right)\)
c,\(x^3+2x^2y-x-2y=\left(x^3+2x^2y\right)-\left(x+2y\right)\)
\(=x^2\left(x+2y\right)-\left(x+2y\right)\)
\(=\left(x^2-1\right)\left(x+2y\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x+2y\right)\)
a)\(9x^2y^3-3x^4y^2-6x^3y^2+18xy^4=3xy^2\left(3xy-x^3-2x^2+6y^2\right)\)
b)\(a^3x^2y^2-\frac{5}{2}a^3x^4+\frac{3}{2}a^4x^2y=a^3x^2\left(y^2-\frac{5}{2}x^2+\frac{3}{2}ay\right)\)
c)\(x^2+4xy-21y^2=\left(x^2+4xy+4y^2\right)-25y^2=\left(x+2y\right)^2-\left(5y\right)^2=\left(x+2y-5y\right)\left(x+2y+5y\right)=\left(x-3y\right)\left(x+7y\right)\)d)\(2x^4+4=2\left(x^4+4\right)=2\left(x^4+4x^2+4-4x^2\right)=2\left[\left(x^2+2\right)^2-\left(2x\right)^2\right]=2\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)
\(y^3-25y+4xy^2+4x^2y=y\left(y^2+4xy+4x^2-25\right)\)
\(=y\left[\left(2x+y\right)^2-25\right]\)
\(=y\left(2x+y+5\right)\left(2x+y-5\right)\)
Câu sau đề không đúng