\(\left(x^2-x+1\right)\left(x^2+3x+1\right)+4x^2\)
\(=\left(x^2+x+1-2x\right)\left(x^2+x+1+2x\right)+4x^2\)
\(=\left(x^2+x+1\right)^2-4x^2+4x^2=\left(x^2+x+1\right)^2\)
\(x^3+5x^2+8x+4\)
\(=x^3+2x^2+3x^2+8x+4\)
\(=x^3+2x^2+3x^2+6x+2x+4\)
\(=x^2\left(x+2\right)+3x\left(x+2\right)+2\left(x+2\right)\)
\(=\left(x^2+3x+2\right)\left(x+2\right)\)
\(=\left(x^2+2x+x+2\right)\left(x+2\right)\)
\(=\left(x+2\right)^2\left(x+1\right)\)
b) \(x^3+5x^2+8x+4=x^3+4x^2+x^2+4x+4x+4\)
\(=\left(x^3+4x^2+4x\right)+\left(x^2+4x+4\right)\)
\(=x\left(x^2+4x+4\right)+\left(x^2+4x+4\right)\)
\(=\left(x^2+4x+4\right)\left(x+1\right)\)
\(=\left(x+2\right)^2\left(x+1\right)\)
Câu a u tự làm nha ! Bận quá nên làm mỗi câu b thôi,thông cảm cho ạ :)
Học Tốt
