Question

Evaluate the expression when$x=4\text{and}y=2$

localid="1648625501579" $2{(x-y)}^2$

Short answer

The value of the expression is8.

Step-by-step solution

Step-1 – Order of operations

To evaluate any expression involving more than one operation, follow the below order of operations:

• First evaluate expressions inside grouping symbols like parentheses ( ) or brackets [ ].
• Evaluate the exponents.
• Perform Multiplication and division from left to right.
• Perform addition and subtraction from left to right.

Step-2 – Evaluate the expression inside grouping symbol

In order to evaluate the given expression, first substitute 4 for x and 2 for y and then subtract the numbers as shown below.

$\begin{array}{l}2{(x-y)}^2\\ =2{(4-2)}^2\\ =2{\left(2\right)}^2\end{array}$

Step-3 – Evaluate the exponent

Now to simplify further, expand the exponent as shown below.

$\begin{array}{l}2{\left(2\right)}^2\\ =2\left(4\right)\end{array}$

Step-4 – Multiply the numbers

Now to simplify further, multiply the resulting numbers to get

$\begin{array}{l}2\left(4\right)\\ =8\end{array}$

Thus, the value of the expression is 8.