The image contains a series of algebraic problems. I will extract and solve each question step by step.

Soru 2: Simplify the given algebraic expressions.

a) $6x + 4x$

$6x + 4x = 10x$

b) $4x^2 - 2x + 7x$

$4x^2 - 2x + 7x = 4x^2 + 5x$

c) $5a^2 - 8a^2$

$5a^2 - 8a^2 = -3a^2$

d) $(x + 9) - (3x + 6)$

$(x + 9) - (3x + 6) = x + 9 - 3x - 6 = -2x + 3$

e) $3x^2 - 5xy + 6 + 3xy - 10$

$3x^2 - 5xy + 6 + 3xy - 10 = 3x^2 - 2xy - 4$

f) $9x \cdot (y + 2)$

This is not simplification but distribution: $9x \cdot (y + 2) = 9xy + 18x$

Soru 3: Perform the multiplications.

a) $4 \cdot (3x - 2)$

$4 \cdot (3x - 2) = 12x - 8$

b) $2 \cdot (5a + 6)$

$2 \cdot (5a + 6) = 10a + 12$

c) $-3a \cdot (2a + 5)$

$-3a \cdot (2a + 5) = -6a^2 - 15a$

d) $(4y - 3) \cdot 2y$

$(4y - 3) \cdot 2y = 8y^2 - 6y$

e) $-2k \cdot (4k - 5k^2)$

$-2k \cdot (4k - 5k^2) = -8k^2 + 10k^3$

f) $(x + 1) \cdot (2x + 2)$

$(x + 1) \cdot (2x + 2) = 2x^2 + 2x + 2x + 2 = 2x^2 + 4x + 2$

Soru 4: Find the expansions.

a) $(x + 3)^2$

$(x + 3)^2 = x^2 + 6x + 9$

b) $(2a - 4)^2$

$(2a - 4)^2 = 4a^2 - 16a + 16$

c) $(x - 2)^2$

$(x - 2)^2 = x^2 - 4x + 4$

g) $x^2 - 4$

This is a difference of squares: $x^2 - 4 = (x - 2)(x + 2)$

h) $a^2 - 1$

This is a difference of squares: $a^2 - 1 = (a - 1)(a + 1)$

i) $36a^2 - 16b^2$

This is a difference of squares: $36a^2 - 16b^2 = (6a - 4b)(6a + 4b)$

Soru 5: Factorize the expressions.

a) $2x + 6$

$2x + 6 = 2(x + 3)$

b) $6a + 12$

$6a + 12 = 6(a + 2)$

c) $4m - 14$

$4m - 14 = 2(2m - 7)$

i) $x \cdot (x + 1) + y \cdot (x + 1)$

Factorize $(x + 1)$: $x \cdot (x + 1) + y \cdot (x + 1) = (x + 1)(x + y)$

j) $a \cdot (x - 2) - b \cdot (x - 2)$

Factorize $(x - 2)$: $a \cdot (x - 2) - b \cdot (x - 2) = (x - 2)(a - b)$

k) $3 \cdot (a - 5) + x \cdot (5 - a)$

Simplify and factorize: $3 \cdot (a - 5) + x \cdot (5 - a) = 3(a - 5) - x(a - 5) = (a - 5)(3 - x)$

Would you like any part of this explanation expanded?
Here are 5 related questions for practice:

1. How do you simplify an algebraic expression with multiple variables?
2. Can you provide the general formula for expanding $(a + b)^2$?
3. How do you recognize and factorize a difference of squares?
4. What steps are involved in distributing a single term into parentheses?
5. How do you factorize expressions with multiple common factors?

Tip: When expanding or factorizing, always double-check your terms to avoid sign errors!