Show that `F: RxxR->R`given by `(a ,b)->a+4b^2`is a binary operation.

Explanation

To show that the function \( F: \mathbb{R} \times \mathbb{R} \to \mathbb{R} \) defined by \( F(a, b) = a + 4b^2 \) is a binary operation, we need to verify that for any \( a, b \in \mathbb{R} \), the output \( F(a, b) \) is also a real number.

### Step-by-Step Solution:

1. **Understanding the Definition of a Binary Operation**:
A binary operation on a set is a function that combines two elements of the set to produce another element of the same set. In this case, we are working with the set of real numbers \( \mathbb{R} \).

2. **Identifying the Inputs and Outputs**:
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