Question

phân tích : a) x^2 + y^2 -z^2 -9t^2-2xy+6zt

b) x^3z +x^2yz-x^2z^2-xyz^2

c) x^4+3x^3-9x-9

d) x^4 +3x^3-9x-27

e) x^3-3x^2+3x-1-8y^3

Answer 1

a: \(=x^2-2xy+y^2-\left(z^2-6zt+9t^2\right)\)

\(=\left(x-y\right)^2-\left(z-3t\right)^2\)

\(=\left(x-y-z+3t\right)\left(x-y+z-3t\right)\)

c: \(=\left(x^4-9\right)+3x\left(x^2-3\right)\)

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

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

d: \(x^4+3x^3-9x-27\)

\(=x^3\left(x+3\right)-9\left(x+3\right)\)

\(=\left(x+3\right)\left(x^3-9\right)\)