Question

phân tích đa thức thành nhân tử bài (x+y)^5-x^5-y^5

Answer 1

Ta có:

\(\left(x+y\right)^5-x^5-y^5=\left(x+y\right)^5-\left(x^5+y^5\right)\)

\(=\left(x+y\right)^5-\left(x+y\right)\left(x^4-x^3y+x^2y^2-xy^3+y^4\right)\)

\(=\left(x+y\right)\left[\left(x+y\right)^4-x^4+x^3y-x^2y^2+xy^3-y^4\right]\)

\(=\left(x+y\right)\left[x^4+4x^3y+6x^2y^2+4xy^3+y^4-x^4+x^3y-x^2y^2+xy^3-y^4\right]\)

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

Answer 2

A = ( x + y )⁵ - x⁵ - y⁵

A = ( x⁵ + 5x⁴y + 10x³y² + 10x²y³ + 5xy⁴ + y⁵ ) - x⁵ - y⁵

A = 5x⁴y + 10x³y² + 10x²y³ + 5xy⁴

A = 5xy( x³ + 2x²y + 2xy² + y³ )

A = 5xy[ ( x + y )( x² - xy + y² ) + 2xy( x + y ) ]

A = 5xy( x + y )( x² + xy + y² )