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\(=6x\left(-y^2+x^2+2x+1\right)\\ =6x\left[\left(x^2+2x+1\right)-y^2\right]\\ =6x\left[\left(x+1\right)^2-y^2\right]\\ =6x\left(x+1-y\right)\left(x+1+y\right)\)
\(x^4+6x^3+13x^2+12x+4\)
\(=x^4+x^3+5x^3+5x^2+8x^2+8x+4x+4\)
\(=x^3\left(x+1\right)+5x^2\left(x+1\right)+8x\left(x+1\right)+4\left(x+1\right)\)
\(=\left(x+1\right)\left(x^3+5x^2+8x+4\right)\)
\(=\left(x+1\right)\left(x^3+x^2+4x^2+4x+4x+4\right)\)
\(=\left(x+1\right)\left[x^2\left(x+1\right)+4x\left(x+1\right)+4\left(x+1\right)\right]\)
\(=\left(x+1\right)^2\left(x+2\right)^2\)
\(a,3x^2-6x+9x^2=12x^2-6x=6x\left(2x-1\right)\\ b,3x^2+5y-3xy-5x=\left(3x^2-3xy\right)-\left(5x-5y\right)=3x\left(x-y\right)-5\left(x-y\right)=\left(x-y\right)\left(3x-5\right)\\ c,3y^2-3z^2+3x^2+6xyz=3\left(y^2-z^2+x^2+2xyz\right)\\ d,x^2-25-2xy+y^2=\left(x-y\right)^2-5^2=\left(x-y-5\right)\left(x-y+5\right)\)
a,\(14x^2y-21xy=7xy.\left(2x-3\right)\)
b,\(-x^2+6x-9=-\left(x^2-6x+9\right)=-\left(x-3\right)^2\)
c,\(3x^2-6xy+3y^2-27=3.\left(x^2-2xy+y^2-9\right)=3.\text{[}\left(x-y\right)^2-3^2\text{]}=3.\left(x-y-3\right).\left(x-y+3\right)\)
a) 14x2y - 21xy
= 7xy (2x - 3)
b) -x2 + 6x - 9
= -(x2 - 6x + 32)
= -(x - 3)2
c) 3x2 - 6xy + 3y2 - 27
= 3 (x2 - 2xy + y2 - 9)
= 3 [(x2 - 2xy + y2) - 9]
= 3 [(x - y)2 - 32]
= 3 (x - y - 3) (x - y + 3)
#Học tốt!!!
~NTTH~
a, 2x3-6x2y+6xy2-2y3
=2(x3-3x2y+3xy2-y3)
=2(x-y)3
b,3x-4x2=0
x(3-4x)=0
=>x=0; 3-4x=0
..................................
\(a.=x^3+3x^2y+3x^2y+9xy^2+3xy^2+9y^3\)
\(=x^2\left(x+3y\right)+3xy\left(x+3y\right)+3y^2\left(x+3y\right)\)
\(=\left(x+3y\right)\left(x^2+3xy+3y^2\right).\)
\(b.=9x^3+3x^2y+9x^2y+3xy^2+3xy^2+y^3\)
\(=3x^2\left(3x+y\right)+3xy\left(3x+y\right)+y^2\left(3x+y\right)\)
\(=\left(3x^2+3xy+y^2\right)\left(3x+y\right)\).
=6x(y-1)
\(6xy-6x\)
\(6\left(xy-x\right)\)
\(x\left(y-1\right)\)
\(6x\left(y-1\right)\)