Q26. - Algebra 1

Question

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

$\left(a^2+2bc\right)÷7$

Step-by-Step Solution

Answer

The value of the given expression is $10$.

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.

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