To expand \((x+5)(x+2)\), use the distributive property (often called the FOIL method for binomials):

\[
(x+5)(x+2) = x \cdot x + x \cdot 2 + 5 \cdot x + 5 \cdot 2
\]

Now calculate each term:

1. \( x \cdot x = x^2 \)
2. \( x \cdot 2 = 2x \)
3. \( 5 \cdot x = 5x \)
4. \( 5 \cdot 2 = 10 \)

Combine all terms:

\[
x^2 + 2x + 5x + 10 = x^2 + 7x + 10
\]

So, the expanded form is:

\[
(x+5)(x+2) = x^2 + 7x + 10
\]

Would you like further details or have any questions?

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Here are 5 related questions to explore further:

1. How would you expand \((x+3)(x+4)\)?
2. What is the expanded form of \((x+1)(x-1)\)?
3. How would you solve the equation \((x+5)(x+2) = 0\)?
4. What is the general formula for expanding \((x+a)(x+b)\)?
5. How can you factor the expression \(x^2 + 7x + 10\) back into two binomials?

**Tip:** Remember, FOIL (First, Outer, Inner, Last) is useful for expanding binomials quickly!

Learn how to expand the expression (x+5)(x+2) using the distributive property, often called FOIL for binomials. This step-by-step guide covers key algebraic concepts and methods, ideal for students in Grades 8-10.

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