Expand the Expression: Solving (x+x²)² Step-by-Step

$(x+x^2)^2=$

To solve this problem, follow these steps:

• Step 1: Identify the terms: Here, $a = x$ and $b = x^2$.
• Step 2: Apply the square of a binomial formula: $(a + b)^2 = a^2 + 2ab + b^2$.
• Step 3: Substitute the terms into the formula and simplify the resulting expression.

Now, let's work through each step:

Step 1: We have $a = x$ and $b = x^2$.
Step 2: The formula gives us: $(a + b)^2 = a^2 + 2ab + b^2$

Step 3: Substituting $a = x$ and $b = x^2$ into the formula:

This simplifies to:

Therefore, the expanded form of the expression $(x + x^2)^2$ is $\mathbf{x^2 + 2x^3 + x^4}$.

This matches with choice 3 from the options provided.