Question

(x+2y-z)square. Expand this by giving showing the method or step....

Answer 1

(X+2y-z)²
=(X+2y-z)(X+2y-z)
=X(X+2y-z)+2y(X+2y-z)+z(X+2y-z)
=x²+2xy-xz+2xy+4y²-2yz+xz+2yz-z²
=x²+4y²-z²+4xy

Answer 2

Given:

$(x+2y-z)^2$

We have to expand the given expression.

Solution:

∴ $(x+2y-z)^2$

= (x +2y - z)(x +2y - z)

= x(x +2y - z) +2y(x +2y - z) - z(x +2y - z)

= $x^{2}$ + 2xy - xz + 2xy + 4$y^{2}$ - 2yz - zx - 2yz + $z^{2}$

= $x^{2}$ + 4$y^{2}$ + $z^{2}$ + (2xy + 2xy) - (2yz + 2yz) - ( xz + xz)

= $x^{2}$ + 4$y^{2}$ + $z^{2}$ + 4xy - 4yz - 2xz

= $x^{2}$ + 4$y^{2}$ + $z^{2}$ + 2(2xy - 2yz - xz)

∴ The expandation of $(x+2y-z)^2$ = $x^{2}$ + 4$y^{2}$ + $z^{2}$ + 2(2xy - 2yz - xz)

Thus, the expandation of $(x+2y-z)^2$ is equal to "$x^{2}$ + 4$y^{2}$ + $z^{2}$ + 2(2xy - 2yz - xz)".