Question

Phân Tích đa thức thành nhân tử

A= (x+y+z)³-x³-y³-z³

 

Answer 1

= x³ + y³ + z³ + 3(x + y )(y+z)(z + x) - x³- y³ - z³

= 3(x + y)(y + z)(z + x)

Answer 2

a, x^4 - 5x^2 + 4

= x^4 - 4x^2- x+ 4

= x^2  . (x^2 - 4) - (x^2 - 4)

= (x^2 - 4) . (x^2 - 1)

= (x - 2) . (x + 2) . (x - 1) . (x + 1)

Answer 3

\(\left(x+y+z\right)^3-x^3-y^3-z^3\)

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

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

\(=3\left(x+y\right)\left(xy+xz+yz+z^2\right)\)

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