a) \(3x^2-\frac{1}{3}y^2+\frac{2}{3}y-\frac{1}{3}\)
\(=\frac{1}{3}.\left(9x^2-y^2+2y-1\right)\)
\(=\frac{1}{3}.\left[9x^2-\left(y^2-2y+1\right)\right]\)
\(=\frac{1}{3}.\left[9x^2-\left(y-1\right)^2\right]\)
\(=\frac{1}{3}.\left[\left(3x\right)^2-\left(y-1\right)^2\right]\)
\(=\frac{1}{3}.\left(3x-y+1\right).\left(3x+y-1\right)\)
b) \(x^3-5x^2+8x-4\)
\(=x^3-4x^2-x^2+4x+4x-4\)
\(=\left(x^3-4x^2+4x\right)-\left(x^2-4x+4\right)\)
\(=x.\left(x^2-4x+4\right)-\left(x^2-4x+4\right)\)
\(=\left(x^2-4x+4\right).\left(x-1\right)\)
\(=\left(x^2-2.x.2+2^2\right).\left(x-1\right)\)
\(=\left(x-2\right)^2.\left(x-1\right)\)
Chúc bạn học tốt!
