(x+5)(x−3)

(y−4)(y+6)(y - 4)(y + 6)(y−4)(y+6)

(2x+1)(x−7)(2x + 1)(x - 7)(2x+1)(x−7)

(a−2)(a+3)(a - 2)(a + 3)(a−2)(a+3)

(3x−2)(x+4)(3x - 2)(x + 4)(3x−2)(x+4)

Let's expand each of the expressions one by one:

1. **(x + 5)(x − 3):**
   - Expand:
     \[
     (x + 5)(x − 3) = x^2 − 3x + 5x − 15
     \]
     Simplified:
     \[
     x^2 + 2x − 15
     \]

2. **(y − 4)(y + 6):**
   - Expand:
     \[
     (y − 4)(y + 6) = y^2 + 6y − 4y − 24
     \]
     Simplified:
     \[
     y^2 + 2y − 24
     \]

3. **(2x + 1)(x − 7):**
   - Expand:
     \[
     (2x + 1)(x − 7) = 2x^2 − 14x + x − 7
     \]
     Simplified:
     \[
     2x^2 − 13x − 7
     \]

4. **(a − 2)(a + 3):**
   - Expand:
     \[
     (a − 2)(a + 3) = a^2 + 3a − 2a − 6
     \]
     Simplified:
     \[
     a^2 + a − 6
     \]

5. **(3x − 2)(x + 4):**
   - Expand:
     \[
     (3x − 2)(x + 4) = 3x^2 + 12x − 2x − 8
     \]
     Simplified:
     \[
     3x^2 + 10x − 8
     \]

Would you like further details or clarifications on any of these expansions?

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Here are 5 related questions:
1. What are the roots of \(x^2 + 2x − 15\)?
2. How do you factor \(y^2 + 2y − 24\)?
3. What is the vertex of the quadratic function \(2x^2 − 13x − 7\)?
4. Can you solve \(a^2 + a − 6 = 0\) by factoring?
5. What are the solutions of \(3x^2 + 10x − 8 = 0\) using the quadratic formula?

**Tip:** Always check for common factors before expanding or simplifying polynomial expressions, as this can simplify your calculations.

Explore how to expand and simplify polynomial expressions like (x + 5)(x − 3), (y − 4)(y + 6), (2x + 1)(x − 7), (a − 2)(a + 3), and (3x − 2)(x + 4). This detailed guide includes step-by-step solutions, focusing on algebraic concepts and polynomial expansion formulas.

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