Question

The expansion of ($x-y+2z{)}^2$ is _______.

• A. $x^2+y^2+4z^2-2xy-4yz+4xz$
• B. $4x^2+y^2+4z^2-4xy-4yz+4xz$
• C. $x^2+y^2+4z^2+4xy-4yz+4xz$
• D. $x^2+4y^2+z^2-2xy-4yz+4xz$

Answer 1

The correct option is A $x^2+y^2+4z^2-2xy-4yz+4xz$

Using the identity $(a+b+c{)}^2$ = $a^2+b^2+c^2+2ab+2bc+2ca$,

($x-y+2z{)}^2$ = $(x{)}^2+(-y{)}^2+(2z{)}^2+2(x\left)\right(-y)+2(-y\left)\right(2z)+2(2z\left)\right(x)$ ,

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