Question

Expand the following:

$\left(iv\right)(\text{x}-3\text{y}-2\text{z}{)}^2$

Answer 1

Given: Expression is $(\text{x}-3\text{y}-2\text{z}{)}^2$

Now, expand the given expression by using the sum of square identity

$(\text{a}+\text{b}+\text{c}{)}^2={\text{a}}^2+{\text{b}}^2+{\text{c}}^2+2\text{a}\text{b}+2\text{b}\text{c}+2\text{c}\text{a}$.

$\Rightarrow (\text{x}-3\text{y}-2\text{z}{)}^2={\text{x}}^2+(-3\text{y}{)}^2+(-2\text{z}{)}^2+2\times \text{x}\times (-3\text{y})+2\times (-3\text{y})\times (-2\text{z})+2\times \text{x}\times (-2\text{z})$

$={\text{x}}^2+9{\text{y}}^2+4{\text{z}}^2-6\text{x}\text{y}+12\text{y}\text{z}-4\text{x}\text{z}$

Hence, expansion of $(\text{x}-3y-2z{)}^2$ is
${\text{x}}^2+9{\text{y}}^2+$ $4{\text{z}}^2-6\text{x}\text{y}+12\text{y}\text{z}-4\text{x}\text{z}$.