Question

Evaluate each expression if $a=4,b=3$and $c=9$.

$\left(a^2+2bc\right)÷7$

Short answer

The value of the given expression is $10$.

Step-by-step solution

Step 1. Method of applying order of operations.

1. Evaluate expressions inside grouping symbols.
2. Evaluate all powers.
3. Multiply and/or divide in order from left to right.
4. Add or subtract in order from left to right.

Step 2. Putting the values of given variables in the expression.

$\left(a^2+2bc\right)÷7=\left(4^2+2·3·9\right)÷7\left[\mathrm{since}a=4,b=3,c=9\right]$

Step 3. Solving bracket.

$$\begin{gathered} \left(4^2+2·3·9\right)÷7=\left(16+2·3·9\right)÷7\left[\mathrm{Evaluating}\mathrm{power}\right] \\ =\left(16+54\right)÷7\left[\mathrm{Performing}\mathrm{multiplication}\right] \\ =70÷7\left[\mathrm{Performing}\mathrm{addition}\right] \end{gathered}$$

Step 4. Simplifying the expression.

$70÷7=10\left[\mathrm{Performing}\mathrm{division}\right]$