How is multiplying radical

expression similar to FOIL with
binomials?

Check my answer to your previous post.

What is still unclear?

Multiplying radical expressions is similar to using the FOIL method with binomials because both involve multiplying pairs of terms to get a simplified expression.

The FOIL method is commonly used when multiplying two binomials. It stands for First, Outer, Inner, and Last. This method requires multiplying the terms in specific order: first the first terms, then the outer terms, then the inner terms, and finally the last terms. Adding these four products together results in the simplified expression.

Similarly, when multiplying radical expressions, you need to multiply the terms of each radical together to simplify the expression. To do this, multiply the first terms, then the outer terms, then the inner terms, and finally the last terms. Once you have these products, add them together to simplify the expression.

Here is a step-by-step example to illustrate the similarities:

Let's consider the expression: √a * √b

Step 1: Multiply the first terms:
√a * √b = √(a * b)

Step 2: Multiply the outer terms:
√a * √b = √a * √b

Step 3: Multiply the inner terms:
√a * √b = √a * √b

Step 4: Multiply the last terms:
√a * √b = √a * √b

Step 5: Simplify by adding the four products:
√a * √b = √(a * b) + (√a * √b) + (√a * √b) + (√a * √b)

Step 6: Combine like terms:
√a * √b = √(a * b) + 2√(a * b)

As you can see, in both processes, you multiply each term with each term and then combine your results to simplify the expression. The FOIL method is just a specific application of multiplying binomials, while multiplying radical expressions follows a similar concept.