Question

Evaluate each expression if $g=2$, $r=3$and $t=11$.

$t^2+8rt+r^2$

Short answer

The value of the expression ${\mathit{t}}^{\mathbf{2}}\mathbf{+}\mathbf{8}\mathit{r}\mathit{t}\mathbf{+}{\mathit{r}}^{\mathbf{2}}$is 394.

Step-by-step solution

Step 1. Evaluation of algebraic expression.

In order to evaluate an expression, substitute the values for the variables and simplify using the order of operations. The order of operations is in order:

1. Evaluate the expressions inside the bracket
2. Evaluate the powers
3. Multiply and/or divide
4. Add and/ or subtract

The evaluation takes place from left to right.

Step 2. Replace the variables.

Substitute 2 for g, 3 for r, and 11 for t into the equation $t^2+8rt+r^2$.

$t^2+8rt+r^2={11}^2+8\cdot 3\cdot 11+3^2$

Step 3. Apply the order of operations.

As per the order of operations, first, evaluate the powers followed by other operations.

$\begin{array}{l}{t}^2+8rt+r^2={11}^2+8\cdot 3\cdot 11+3^2\\ =121+8\cdot 3\cdot 11+9\\ =121+264+9\\ =394\end{array}$

Therefore, the expression is equal to 394.