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Let's solve the given algebraic expressions step-by-step by substituting the values:

### Part (a)
Expression: \( 6 + 4(x - 4)^3 \), for \( x = 6 \)

1. Substitute \( x = 6 \):
   \[
   6 + 4(6 - 4)^3
   \]

2. Simplify inside the parentheses:
   \[
   6 - 4 = 2
   \]

3. Raise to the power of 3:
   \[
   2^3 = 8
   \]

4. Multiply by 4:
   \[
   4 \times 8 = 32
   \]

5. Add 6:
   \[
   6 + 32 = 38
   \]

**Answer for (a):** 38

### Part (b)
Expression: \( x^2 - 2(x - y) \), for \( x = 9 \) and \( y = 3 \)

1. Substitute \( x = 9 \) and \( y = 3 \):
   \[
   9^2 - 2(9 - 3)
   \]

2. Calculate \( 9^2 \):
   \[
   9^2 = 81
   \]

3. Simplify inside the parentheses:
   \[
   9 - 3 = 6
   \]

4. Multiply by 2:
   \[
   2 \times 6 = 12
   \]

5. Subtract from 81:
   \[
   81 - 12 = 69
   \]

**Answer for (b):** 69

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Would you like any further details or have any questions?

Here are some related questions that might help you practice similar problems:

1. Evaluate \( 5 + 3(x + 1)^2 \) for \( x = 2 \).
2. Find the value of \( 2x^3 - y^2 \) for \( x = 4 \) and \( y = 5 \).
3. Simplify the expression \( 7 - 2(x - 3)^2 \) when \( x = 1 \).
4. Evaluate \( x^2 + y - z \) for \( x = 7 \), \( y = 5 \), and \( z = 3 \).
5. Calculate \( 3(x - 2)^3 + 4y \) for \( x = 3 \) and \( y = 2 \).

**Tip:** Always simplify the expression inside the parentheses before proceeding with powers or multiplication to reduce mistakes.

Evaluate the algebraic expressions: a) 6 + 4(x - 4)^3 for x = 6; b) x^2 - 2(x - y) for x = 9 and y = 3

Learn how to evaluate algebraic expressions like 6 + 4(x - 4)^3 for x = 6 and x^2 - 2(x - y) for x = 9 and y = 3 with step-by-step solutions. This problem covers key algebraic concepts, including exponents and substitution, suitable for Grades 7-9.

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