# 7.2.1. Algebraic Terms and Algebraic Expressions

Given the figure below, write the algebraic expression that represents the area of the shaded region, then state its degree, considering the area of the circle .

• A The expression , and it is of the second degree.
• B The expression , and it is of the first degree.
• C The expression , and it is of the second degree.
• D The expression , and it is of the first degree.

### Example

Given the figure below, write the algebraic expression that represents the area of the shaded region, then state its degree, considering the area of the circle .

### Solution

Step 1: Find the algebraic expression that represents the area of the triangle.

So, the algebraic expression represents the area of the triangle.

Step 2: Find the algebraic expression that represents the area of the shaded region.

Subtract the area or the circle from the area of the triangle. So, the expression represents the area of the shaded region.

Step 3: Determine the degree of the algebraic expression .

The degree of an algebraic expression with several terms is equal to the highest degree of the terms that form it. The degree of each term is the sum of the indices (powers) of the algebraic factors.

The first term has a degree of 2 because (adding the powers of and ). The second term also has a degree of 2 because the power of is 2.

Since the highest degree of the terms is 2, therefore the algebraic expression is of the second degree.

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