https://file.aiquickdraw.com/mathbot/file/17282568630464bwxxc89.jpg

The expression in the image is:

\[
(5 + \sqrt{11})(2 + \sqrt{11})
\]

To solve this, we can expand it using the distributive property (also known as the FOIL method for binomials):

\[
(5 + \sqrt{11})(2 + \sqrt{11}) = 5 \cdot 2 + 5 \cdot \sqrt{11} + \sqrt{11} \cdot 2 + \sqrt{11} \cdot \sqrt{11}
\]

Calculating each term:
1. \( 5 \cdot 2 = 10 \)
2. \( 5 \cdot \sqrt{11} = 5\sqrt{11} \)
3. \( \sqrt{11} \cdot 2 = 2\sqrt{11} \)
4. \( \sqrt{11} \cdot \sqrt{11} = 11 \)

Now, combine all these results:
\[
10 + 5\sqrt{11} + 2\sqrt{11} + 11
\]

Simplify by combining like terms:
\[
(10 + 11) + (5\sqrt{11} + 2\sqrt{11}) = 21 + 7\sqrt{11}
\]

So, the expanded form of the expression is:
\[
21 + 7\sqrt{11}
\]

Would you like more details on this process or have any questions?

Here are some related questions you might consider:
1. How do you multiply expressions with square roots?
2. What is the FOIL method and when is it used?
3. How do you simplify expressions involving square roots?
4. What are some common mistakes to avoid when expanding binomials?
5. How can you use the distributive property in algebraic expressions?

**Tip:** When multiplying binomials, always ensure you handle each term systematically to avoid missing any terms!

Learn how to expand and simplify the binomial expression (5 + √11)(2 + √11) using the FOIL method. This problem demonstrates the use of square roots and the distributive property. Suitable for high school students in Grades 9-12.

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