Evaluating the Expression ((-1)^2 + 11^2)(11^2 - {(-7)}^2)

As a high school mathematics teacher, I often encounter questions that involve evaluating complex mathematical expressions. One such expression is ((-1)^2 + 11^2)(11^2 - {(-7)}^2). Let's break down this expression and evaluate it step by step.

Step 1: Evaluate the Inner Expressions

We'll start by evaluating the inner expressions within the parentheses.

1. (-1)^2: This is the exponentiation of -1 to the power of 2. The result of this operation is 1, as any number raised to the power of 2 is its square.

2. 11^2: This is the exponentiation of 11 to the power of 2. The result of this operation is 121, as 11 squared is 121.

3. {(-7)}^2: This is the exponentiation of -7 to the power of 2. The result of this operation is 49, as -7 squared is 49.

Step 2: Evaluate the Outer Expressions

Now that we have the results of the inner expressions, we can proceed to evaluate the outer expressions.

1. ((-1)^2 + 11^2): This is the addition of 1 (from (-1)^2) and 121 (from 11^2), which results in 122.

2. (11^2 - {(-7)}^2): This is the subtraction of 49 (from {(-7)}^2) from 121 (from 11^2), which results in 72.

Step 3: Multiply the Outer Expressions

Finally, we multiply the two outer expressions to get the final result.

((-1)^2 + 11^2)(11^2 - {(-7)}^2) = 122 × 72 = 8,784

Therefore, the value of the expression ((-1)^2 + 11^2)(11^2 - {(-7)}^2) is 8,784.