Question

phân tích đa thức thành nhân tử

d, \(5x+5y-x^2-2xy-y^2\)

e,\(x^5-x^4+x^3-x^2\)

hepl me Nguyễn Huy Tú

Answer 1

d, \(5x+5y-x^2-2xy-y^2\)

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

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

e, \(x^5-x^4+x^3-x^2\)

\(=x^4\left(x-1\right)+x^2\left(x-1\right)\)

\(=\left(x^4+x^2\right)\left(x-1\right)\)

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

Answer 2

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

\(x^5-x^4+x^3-x^2\\ =x^4\left(x-1\right)+x^2\left(x-1\right)\\ \left(x^4+x^2\right)\left(x-1\right)\\ =x^2\left(x^2+1\right)\left(x-1\right)\)