a, \(x^3-x^2y-xy^2+y^3\)
\(=x^2\left(x-y\right)-y^2\left(x-y\right)\)
\(=\left(x^2-y^2\right)\left(x-y\right)\)
\(=\left(x-y\right)^2\left(x+y\right)\)
b, \(x^3+x^2-4x-4\)
\(=x^2\left(x+1\right)-4\left(x+1\right)\)
\(=\left(x^2-4\right)\left(x+1\right)=\left(x-2\right)\left(x+2\right)\left(x+1\right)\)
c, \(x^3-x^2-x+1\)
\(=x^2\left(x-1\right)-\left(x-1\right)=\left(x^2-1\right)\left(x-1\right)\)
\(=\left(x-1\right)^2\left(x+1\right)\)
d, \(\left(7x+3\right)^2-\left(2x-1\right)^2\)
\(=\left(7x+3-2x+1\right)\left(7x+3+2x-1\right)\)
\(=\left(5x+4\right)\left(9x+2\right)\)
e, \(x^3-3x^2-3x+1\) sai đề
f, \(x^2-2x-3\)
\(=x^2-3x+x-3=x\left(x-3\right)+\left(x-3\right)\)
\(=\left(x+1\right)\left(x-3\right)\)
g, \(x^2-2x-8\)
\(=x^2-4x+2x-8=x\left(x-4\right)+2\left(x-8\right)\)
\(=\left(x+2\right)\left(x-8\right)\)
h, \(x^2-10x+21\)
\(=x^2-7x-3x+21\)
\(=x\left(x-7\right)-3\left(x-7\right)=\left(x-3\right)\left(x-7\right)\)
i, \(x^2-4xy+3y^2\)
\(=x^2-4xy+4y^2-y^2\)
\(=\left(x-2y\right)^2-y^2\)
\(=\left(x-2y-y\right)\left(x-2y+y\right)\)
\(=\left(x-3y\right)\left(x-y\right)\)
a) \(x^3 - x^2y - xy^2 + y^3\)
\(=\left(x^3-x^2y\right)-\left(xy^2-y^3\right)\)
\(=x^2\left(x-y\right)-y^2\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2-y^2\right)\)
\(=\left(x-y\right)\left(x-y\right)\left(x+y\right)\)
\(=\left(x-y\right)^2\left(x+y\right)\)
b) \(x^3 + x^2 - 4x - 4\)
\(=\left(x^3+x^2\right)-\left(4x+4\right)\)
\(=x^2\left(x+1\right)-4\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-4\right)\)
\(=\left(x+1\right)\left(x^2-2^2\right)\)
\(=\left(x+1\right)\left(x+2\right)\left(x-2\right)\)
