Calculate the Square's Area Using the Expression (x+1)²

To find the area of a square with side length $x + 1$, we apply the formula for the area of a square, which is side squared. This means we need to calculate $(x + 1)^2$.

Here are the steps to solve the problem:

• Step 1: Identify the expression for the side length. The side length of the square is given as $x + 1$.
• Step 2: Use the formula for the area of a square: $(\text{side})^2$.
• Step 3: Substitute the side length with $x + 1$: $(x + 1)^2$.
• Step 4: Expand the expression using the formula for the square of a sum: $(a + b)^2 = a^2 + 2ab + b^2$, where $a = x$ and $b = 1$.
• Step 5: Calculation:
• $(x + 1)^2 = x^2 + 2(x)(1) + 1^2$
• $(x + 1)^2 = x^2 + 2x + 1$

Therefore, the algebraic expression for the area of the square is $x^2 + 2x + 1$.