Question

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

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

Answer 1

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

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

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

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