Question

The expansion of $(x+2y+3z{)}^2$ is :

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

Answer 1

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

Using the identity
$(a+b+c{)}^2=a^2+b^2+c^2+2ab+2bc+2ca$,
$(x+2y+z{)}^2=(x{)}^2+(2y{)}^2+(3z{)}^2+2\left(x\right)\left(2y\right)+2\left(2y\right)\left(3z\right)+2\left(3z\right)\left(x\right)$
$=x^2+4y^2+9z^2+4xy+12yz+6xz$.