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!