Expand and simpilfy
a) ($$ x $$-3)($$ x $$+7)
b) ($$ x $$+2)$$ ^2 $$
c) (2$$ x+4)\left(x+6\right) $$

Let's expand and simplify each expression step by step:

### a) $(x - 3)(x + 7)$

We can apply the **distributive property** (also known as FOIL for binomials) to expand:

\[
(x - 3)(x + 7) = x(x + 7) - 3(x + 7)
\]
\[
= x^2 + 7x - 3x - 21
\]
\[
= x^2 + 4x - 21
\]

### b) $(x + 2)^2$

To expand a binomial squared, we use the formula $(a + b)^2 = a^2 + 2ab + b^2$:

\[
(x + 2)^2 = x^2 + 2(2)(x) + 2^2
\]
\[
= x^2 + 4x + 4
\]

### c) $(2x + 4)(x + 6)$

Again, we apply the **distributive property**:

\[
(2x + 4)(x + 6) = 2x(x + 6) + 4(x + 6)
\]
\[
= 2x^2 + 12x + 4x + 24
\]
\[
= 2x^2 + 16x + 24
\]

### Final Answers:
- a) $ x^2 + 4x - 21 $
- b) $ x^2 + 4x + 4 $
- c) $ 2x^2 + 16x + 24 $

Let me know if you'd like further clarification on any step!

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**Relative Questions:**
1. What is the distributive property in algebra?
2. Can you explain the FOIL method for binomials?
3. How do you expand a binomial square?
4. Why does the order of terms in a multiplication not matter?
5. What is the difference between factoring and expanding?

**Tip:** When expanding polynomials, organizing like terms before simplifying can help avoid mistakes.

Expand and simplify
a) (x - 3)(x + 7)
b) (x + 2)^2
c) (2x + 4)(x + 6)

Learn how to expand and simplify polynomial expressions, including (x - 3)(x + 7), (x + 2)^2, and (2x + 4)(x + 6). This step-by-step guide covers key algebraic concepts such as the distributive property and binomial multiplication. Suitable for students in Grades 8-10.

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