The image you uploaded contains a list of factorization and expansion problems. Let's go through and solve each of them one by one.

Factorization:

1. $x^2 = 9$
   $x^2 - 9 = 0 \quad \text{(Rewrite as a difference of squares)}$ $(x - 3)(x + 3) = 0$ The factorization is: $(x - 3)(x + 3)$

2. $x^2 - 16x$
   Factor out the common term: $x(x - 16)$ The factorization is: $x(x - 16)$

3. $4x^2 - 25x$
   Factor out the greatest common factor (GCF), which is $x$: $x(4x - 25)$ The factorization is: $x(4x - 25)$

4. $x^2 - 100$
   This is a difference of squares: $(x - 10)(x + 10)$ The factorization is: $(x - 10)(x + 10)$

5. $x^3 - 36x$
   Factor out the greatest common factor, $x$: $x(x^2 - 36) = x(x - 6)(x + 6)$ The factorization is: $x(x - 6)(x + 6)$

6. $4x^2 + 6x$
   Factor out the greatest common factor, which is $2x$: $2x(2x + 3)$ The factorization is: $2x(2x + 3)$

7. $x^3 + 4x$
   Factor out the greatest common factor, $x$: $x(x^2 + 4)$ The factorization is: $x(x^2 + 4)$

8. $x^2 - 49$
   This is a difference of squares: $(x - 7)(x + 7)$ The factorization is: $(x - 7)(x + 7)$

Expansion:

1. $(x + 3)^3$
   Use the binomial expansion formula for $(a + b)^3$: $(x + 3)^3 = (x + 3)(x + 3)(x + 3)$ First, expand two terms: $(x + 3)(x + 3) = x^2 + 6x + 9$ Now, multiply the result by $(x + 3)$: $(x^2 + 6x + 9)(x + 3) = x^3 + 3x^2 + 6x^2 + 18x + 9x + 27$ Combine like terms: $x^3 + 9x^2 + 27x + 27$ The expansion is: $x^3 + 9x^2 + 27x + 27$

2. $(2x + 5)(2x - 5)$
   This is a difference of squares: $(2x + 5)(2x - 5) = 4x^2 - 25$ The expansion is: $4x^2 - 25$

Let me know if you need any more detailed explanations!

Related Questions:

1. How can you recognize a difference of squares in an equation?
2. What is the general form of factoring cubic polynomials?
3. What technique is used to factor expressions like $x^2 + bx$?
4. How does the binomial expansion formula work for higher powers?
5. What is the relationship between factoring and solving quadratic equations?

Tip: Always look for a common factor to simplify expressions before attempting more complex factorization techniques!