Question

Expand$(x-2y-3z{)}^2$.

Answer 1

Expanding the given expression:

The given expression is $(x-2y-3z{)}^2$.

Use identity$(a+b+c{)}^2=a^2+b^2+c^2+2ab+2bc+2ca$ to expand.

The given equation can be rewritten as ${\left(x-2y-3z\right)}^2={\left[x+\left(-2y\right)+\left(-3z\right)\right]}^2$

Compare the given expression with the identity we get, $a=x,b=-2y,c=-3z$

Substituting values of $a,b,c$ in identity we get:

$$\begin{gathered} {\left[x+\left(-2y\right)+\left(-3z\right)\right]}^2=x^2+{\left(-2y\right)}^2+{\left(-3z\right)}^2+2\left(x\right)\left(-2y\right)+2\left(-2y\right)\left(-3z\right)+2\left(x\right)\left(-3z\right) \\ =x^2+4y^2+9z^2-4xy+12yz-6xz \end{gathered}$$

Hence, the expression, ${\left(x-2y-3z\right)}^2=x^2+4y^2+9z^2-4xy+12yz-6xz$.