Solve these 3 questions for me:
i.  (2x+3)(x+3)
ii.  (x+3)(x+3)
iii. (x-3)(x+3)

Let's solve each of these expressions:

### i. \((2x + 3)(x + 3)\)
To expand, we use the distributive property:

\[
(2x + 3)(x + 3) = 2x(x) + 2x(3) + 3(x) + 3(3)
\]

Calculating each term:
1. \(2x \cdot x = 2x^2\)
2. \(2x \cdot 3 = 6x\)
3. \(3 \cdot x = 3x\)
4. \(3 \cdot 3 = 9\)

Combine all terms:

\[
2x^2 + 6x + 3x + 9 = 2x^2 + 9x + 9
\]

So, the expanded form is:
\[
2x^2 + 9x + 9
\]

---

### ii. \((x + 3)(x + 3)\)
This is a perfect square expression, so we can expand it as:

\[
(x + 3)(x + 3) = x^2 + 3x + 3x + 9
\]

Combine terms:

\[
x^2 + 6x + 9
\]

So, the expanded form is:
\[
x^2 + 6x + 9
\]

---

### iii. \((x - 3)(x + 3)\)
This is a difference of squares, which follows the formula \((a - b)(a + b) = a^2 - b^2\):

\[
(x - 3)(x + 3) = x^2 - 3^2 = x^2 - 9
\]

So, the expanded form is:
\[
x^2 - 9
\]

---

### Summary of Solutions:
1. \((2x + 3)(x + 3) = 2x^2 + 9x + 9\)
2. \((x + 3)(x + 3) = x^2 + 6x + 9\)
3. \((x - 3)(x + 3) = x^2 - 9\)

Would you like more detailed explanations for any of these steps? 

---

#### 5 Related Questions
1. How would you factor expressions similar to these after expanding?
2. What is the significance of the difference of squares in algebra?
3. How do you identify a perfect square trinomial, and why is it useful?
4. Can these techniques be applied to expressions with more terms, like \((2x+3)(x^2+3x+4)\)?
5. How do you determine if an expression is a difference of squares before expanding?

#### Tip:
When working with binomials, always look for recognizable patterns, like the difference of squares or perfect squares, to simplify your work.

Solve these 3 questions for me:
i. (2x+3)(x+3)
ii. (x+3)(x+3)
iii. (x-3)(x+3)

Expand the binomial expressions (2x+3)(x+3), (x+3)^2, and (x-3)(x+3) with detailed steps. Learn key algebraic concepts, including binomial expansion, the perfect square formula, and the difference of squares theorem. Ideal for Grades 8-10.

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