Question

Chọn đáp án đúng

\({ (x^{3}+3x^{2}y+3xy^{2}+y^{3}-z^{3}):(x+y-z) }\)

\(A. { x^{2}+y^{2}+z^{2}+2xy+xz+yz }\)

\(B. { x^{2}+y^{2}+z^{2}+2xy-xz-yz } \)

\(D. { x^{2}+y^{2}-z^{2}+2xy-xz-yz } \)

Answer 1

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

Vậy chọn A