- Identify the variable value as \(b = 7\).
- Substitute the value into the expression \(4b^2\), resulting in \(4(7)^2\).
- Calculate the square: \(7^2 = 49\).
- Multiply by the coefficient: \(4 \times 49 = 196\).
- Final answer: \(\boxed{196}\)
Explanation
- Problem Analysis and Substitution
The expression to evaluate is \(4b^2\), given the specific value \(b = 7\). The process involves substituting this value into the expression and following the order of operations, which dictates that we perform exponentiation before multiplication.
- Calculation Steps
First, we square the value of \(b\):
\[b^2 = 7^2 = 7 \times 7 = 49.\]
Next, we multiply this result by 4:
\[4b^2 = 4 \times 49 = 196.\]
Thus, the value of the expression \(4b^2\) when \(b=7\) is 196.
Examples
Evaluating algebraic expressions is a foundational skill used in many practical scenarios, such as calculating the area of a square or a circle or determining the cost of goods given a specific quantity and unit price. For example, if you know that the cost of an item follows the formula \(C(n) = 4n^2\), where \(n\) is the number of units, you can determine that for 7 units, the total cost would be \(\$196\). This type of substitution is essential for making informed financial or structural decisions in daily life.