Bài này giải hệ số bất định.

Ta có:

\(x^4-8x+63\)

\(=x^4+4x^3-4x^3+9x^2-16x^2+7x^2-36x+28x+63\)

\(=\left(x^4-4x^3+7x^2\right)+\left(4x^3-16x^2+28x\right)+\left(9x^2-36x+63\right)\)

\(=x^2\left(x^2-4x+7\right)+4x\left(x^2-4x+7\right)+9\left(x^2-4x+7\right)\)

\(=\left(x^2+4x+9\right)\left(x^2-4x+7\right)\)

     \(x^3+xy^2-2y^3\)

\(=x^3-y^3+xy^2-y^3\)

\(=\left(x-y\right)\left(x^2+xy+y^2\right)+y^2\left(x-y\right)\)

\(=\left(x-y\right)\left(x^2+xy+y^2+y^2\right)\)

\(=\left(x-y\right)\left(x^2+xy+2y^2\right)\)

Vậy \(\left(x^3+xy^2-2y^3\right):\left(x-y\right)=x^2+xy+2y^2\)

Chúc bạn học tốt.

\(\left(x-2\right)\left(x^2+2x+4\right)-\left(x-3\right)^3-\left(x-2\right)^3\)

\(=x^3+2x^2+4x-2x^2-4x-8\) \(-\left(x^3-3x^2.3+3x.3^2-27\right)-\)-\(\left(x^3-3.x^2.2+3.x.2^2-8\right)\)

\(=x^3-8\) \(-x^3+9x^2-27x+27-x^3+6x^2-12x+8\)

\(=-x^3+15x^2-39x+27\)

học tốt

\(\left(2y-5x\right)^3+\left(5x+y\right)^3\)

\(=\left[8y^3-3.4y^2.5x+3.2y.25x^2-125x^3\right]\) \(+\left[125x^3+3.25x^2.y+3.5x.y^2+y^3\right]\)

\(=8y^3-60xy^2+150x^2y-125x^3\) \(+125x^3+75x^2y+15xy^2+y^3\)

\(=9y^3-45xy^2+225x^2y\)

học tốt

\(\left(3a-2x\right)^2-\left(a-2x\right)^2\)

\(=\left(3a-2x+a-2x\right)\left(3a-2x-a+2x\right)\)

\(=2a\left(4a-4x\right)\)

\(=8a\left(a-x\right)\)

\(\left(3a-2x\right)^2-\left(a-2x\right)^2=\left(3a-2x+a-2x\right)\left(3a-2x-a+2x\right)\)

\(=\left(4a-4x\right)2a\)

\(=8a.\left(a-x\right)\)

Ta có \(x^3-x^2-5x-3=x^3+x^2-2x^2-2x-3x-3\)

\(=x^2.\left(x+1\right)-2x.\left(x+1\right)-3.\left(x+1\right)\)

\(=\left(x+1\right).\left(x^2-2x-3\right)\)

Do đó \(\left(x^3-x^2-5x-3\right):\left(x+1\right)=\left(x+1\right).\left(x^2-2x-3\right):\left(x+1\right)\)

\(=x^2-2x-3\)