Question

Expand $(x+2y+3z{)}^2$ using algebraic identity.

• A. $x^2+4y^2+9z^2+2xy+2xz+3yz$
• B. $x^2+4y^2+9z^2+xy+xz+yz$
• C. $x^2+2y^2+3z^2+4xy+6xz+12yz$
• D. $x^2+4y^2+9z^2+4xy+6xz+12yz$

Answer 1

The correct option is D $x^2+4y^2+9z^2+4xy+6xz+12yz$

Comparing the given expression with $(x+y+z{)}^2$
We have x = x , y = 2y and z = 3z
Hence using the identity $(x+y+z{)}^2$ = $x^2+y^2+z^2+2xy+2yz+2xz$
We have $(x+2y+3z{)}^2$ =
$\Rightarrow$
$x^2+(2y{)}^2+(3z{)}^2+2\left(x\right)\left(2y\right)+2\left(x\right)\left(3z\right)+2\left(2y\right)\left(3z\right)$

$\Rightarrow$$x^2+4y^2+9z^2+4xy+6xz+12yz$