a. \(x^4-4x^3+8x^2-16x+16\)
\(=x^4-2x^3-2x^3+4x^2+4x^2-8x-8x+16\)
\(=x^3\left(x-2\right)-2x^2\left(x-2\right)+4x\left(x-2\right)-8\left(x-2\right)\)
\(=\left(x-2\right)\left(x^3-2x^2+4x-8\right)\)
\(=\left(x-2\right)\left[x^2\left(x-2\right)+4\left(x-2\right)\right]\)
\(=\left(x-2\right)^2\left(x^2+4\right)\)
b. \(x^4-25x^2+20x-4\)
\(=x^4+5x^3-5x^3-25x^2+2x^2-2x^2+10x+10x-4\)
\(=\left(x^4+5x^3-2x^2\right)-\left(5x^3+25x^2-10x\right)+\left(2x^2+10x-4\right)\)
\(=x^2\left(x^2+5x-2\right)-5x\left(x^2+5x-2\right)+2\left(x^2+5x-2\right)\)
\(=\left(x^2+5x-2\right)\left(x^2-5x+2\right)\)
a, Đặt \(A=x^4-4x^3+8x^2-16x+16\)
=> \(A=x^4-2x^3-2x^3+4x^2+4x^2-8x-8x+16\)
\(\Leftrightarrow A=x^3\left(x-2\right)-2x^2\left(x-2\right)+4x\left(x-2\right)-8\left(x-2\right)\)
\(\Leftrightarrow A=\left(x^3-2x^2+4x-8\right)\left(x-2\right)\)
\(\Leftrightarrow A=\left[x^2\left(x-2\right)+4\left(x-2\right)\right]\left(x-2\right)\)
\(\Leftrightarrow A=\left(x^2+4\right)\left(x-2\right)\left(x-2\right)\)
b,Đặt \(B=x^4-25x^2+20x-4\)
suy ra \(B=x^4+5x^3-2x^2-5x^3-25x^2+10x+2x^2+10x-4\)
\(\Leftrightarrow B=x^2\left(x^2+5x-2\right)-5x\left(x^2+5x-2\right)+2\left(x^2+5x-2\right)\)
\(\Leftrightarrow B=\left(x^2-5x+2\right)\left(x^2+5x-2\right)\)
