https://file.aiquickdraw.com/mathbot/file/1727104747000h12qjshp.jpg

The expression in the image is:

\[
(5 - x) \times (x + 1)
\]

Let's simplify this by applying the distributive property (also known as the FOIL method for binomials):

1. Multiply \( 5 \) by \( x \):
   \[
   5 \times x = 5x
   \]

2. Multiply \( 5 \) by \( 1 \):
   \[
   5 \times 1 = 5
   \]

3. Multiply \( -x \) by \( x \):
   \[
   -x \times x = -x^2
   \]

4. Multiply \( -x \) by \( 1 \):
   \[
   -x \times 1 = -x
   \]

Now, combining all the terms together:
\[
5x + 5 - x^2 - x
\]

Finally, combine like terms:
\[
-x^2 + 4x + 5
\]

So, the simplified expression is:
\[
-x^2 + 4x + 5
\]

Let me know if you want any further details or clarifications!

Here are five related questions to further explore this concept:
1. How would you solve \( (5 - x) \times (x + 1) = 0 \) for \( x \)?
2. What is the factored form of the expression \( -x^2 + 4x + 5 \)?
3. How do you graph the quadratic equation \( y = -x^2 + 4x + 5 \)?
4. Can this expression be solved using the quadratic formula?
5. What is the vertex form of the equation \( -x^2 + 4x + 5 \)?

**Tip:** When expanding binomials, always apply the distributive property carefully, or use the FOIL method for pairs of terms.

Simplify the expression (5 - x) * (x + 1) step-by-step using the distributive property. This algebraic problem involves combining like terms and understanding quadratic equations. Suitable for students in Grades 7-9.

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