Phân tích đa thức thành nhân tử : a) x^4 + 5x^3 + 10x - 4 b) x^4 +y^4 +(x+y) ^4 c) (x-y)^3 + (y -z) ^3 + (z - x) ^3 d) x^4+ 7x^2 - 6x + 1

\[\begin{array}{l} c)\,\,{\left( {x - y} \right)^3} + {\left( {y - z} \right)^3} + {\left( {z - x} \right)^3}\\ = \left( {x - y + y - z} \right)\left[ {{{\left( {x - y} \right)}^2} - \left( {x - y} \right)\left( {y - z} \right) + {{\left( {y - z} \right)}^2}} \right] - {\left( {x - z} \right)^3}\\ = \left( {x - z} \right)\left[ {{{\left( {x - y} \right)}^2} - \left( {x - y} \right)\left( {y - z} \right) + {{\left( {y - z} \right)}^2} - {{\left( {x - z} \right)}^2}} \right]\\ = \left( {x - z} \right)\left\{ {\left[ {{{\left( {x - y} \right)}^2} - {{\left( {x - z} \right)}^2}} \right] - \left[ {\left( {x - y} \right)\left( {y - z} \right) + {{\left( {y - z} \right)}^2}} \right]} \right\}\\ = \left( {x - z} \right)\left[ {\left( {x - y - x + z} \right)\left( {x - y + x - z} \right) - \left( {y - z} \right)\left( {x - y + y - z} \right)} \right]\\ = \left( {x - z} \right)\left[ {\left( {z - y} \right)\left( {2x + y - z} \right) + \left( {z - y} \right)\left( {x - z} \right)} \right]\\ = \left( {x - z} \right)\left( {z - y} \right)\left( {2x + y - z + x - z} \right)\\ = \left( {x - z} \right)\left( {z - y} \right)\left( {3x + y - 2z} \right). \end{array}\] Câu d em đã chép đúng đề bài chưa e?

a) \(x^4+5x^3+10x-4\)

\(=(x^4-4)+(5x^3+10x)\)

\(=(x^2-2)(x^2+2)+5x(x^2+2)\).

b) \(x^4+y^4+[(x+y)^2]^2\)

\(=x^4+y^4+(x^2+y^2+2xy)^2\)

\(=x^4+y^4+x^4+y^4+4x^2y^2+2x^2y^2+4x^3y+4xy^3\)

\(=2x^4+2y^4+6x^2y^2+4x^3y+4xy^3\)

\(=2(x^4+y^4+2x^2y^2)+2x^2y^2+4xy(x^2+y^2)\)

\(=2(x^2+y^2)^2+2x^2y^2+4xy(x^2+y^2)\)

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