Work out the value of these expressions when a = 5, b = 6 and c = −2.
a a
2 + (b – 2c)
2
 (2)
b (3b)
2
 (2)
c ab2 (2)
d
a a c b

Let's break down and solve each expression step by step, using the given values: \( a = 5 \), \( b = 6 \), and \( c = -2 \).

### a) \( a^2 + (b - 2c)^2 \)

1. \( a^2 = 5^2 = 25 \)
2. \( b - 2c = 6 - 2(-2) = 6 + 4 = 10 \)
3. \( (b - 2c)^2 = 10^2 = 100 \)

So the expression becomes:
\[
a^2 + (b - 2c)^2 = 25 + 100 = 125
\]

### b) \( (3b)^2 \)

1. \( 3b = 3 \times 6 = 18 \)
2. \( (3b)^2 = 18^2 = 324 \)

So, the value of the expression is:
\[
(3b)^2 = 324
\]

### c) \( ab^2 \)

1. \( ab^2 = 5 \times 6^2 = 5 \times 36 = 180 \)

So, the value of the expression is:
\[
ab^2 = 180
\]

### d) \( \frac{a \cdot a \cdot c}{b} \)

1. \( a \cdot a \cdot c = 5 \times 5 \times (-2) = -50 \)
2. \( \frac{a \cdot a \cdot c}{b} = \frac{-50}{6} \)

Simplifying:
\[
\frac{-50}{6} \approx -8.33 \quad \text{(rounded to two decimal places)}
\]

### Final Answers:
a) \( 125 \)  
b) \( 324 \)  
c) \( 180 \)  
d) \( -8.33 \) (rounded)

Would you like any further details or clarification on these steps?

Here are 5 related questions to explore further:
1. How would the expressions change if \( c \) were positive?
2. What is the general form of these expressions with variables?
3. How can you simplify the expressions for larger values of \( a \) and \( b \)?
4. Can you derive the derivative of any of these expressions?
5. What happens when \( a = b = c = 0 \)?

**Tip:** Always perform operations inside parentheses first when evaluating complex expressions.

Work out the value of these expressions when a = 5, b = 6 and c = −2.
a) a^2 + (b - 2c)^2
b) (3b)^2
c) ab^2
d) (a * a * c) / b

Solve the expressions a^2 + (b - 2c)^2, (3b)^2, ab^2, and (a * a * c) / b by substituting values a = 5, b = 6, and c = -2. Learn how to calculate powers and perform operations step by step. Suitable for students in Grades 7-9.

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