Chapter 11.9, Problem 46WE

To determine

Simplify.

Answer to Problem 46WE

The simplified form of ${\left(x-3\sqrt{2}\right)}^2$ is $x^2+18-6\sqrt{2}x$ .

Explanation of Solution

Given information:

The expression ${\left(x-3\sqrt{2}\right)}^2$ .

Formula used:

  ${\left(a-b\right)}^2=a^2+b^2-2ab$

  ${\left(x-3\sqrt{2}\right)}^2$

As the expression resembles ${\left(a-b\right)}^2$ ,

we will use identity ${\left(a-b\right)}^2=a^2+b^2-2ab$

  $\begin{array}{l}{\left(x-3\sqrt{2}\right)}^2\\ =x^2+{\left(3\sqrt{2}\right)}^2-2\cdot x\cdot 3\sqrt{2}\\ =x^2+9\cdot 2-6\sqrt{2}x\\ =x^2+18-6\sqrt{2}x\end{array}$

The simplified form of ${\left(x-3\sqrt{2}\right)}^2$ is $x^2+18-6\sqrt{2}x$ .