EXERCISES: Perform the indicated operations using the rules for special products (not FOIL).

1. (x - 2) ^ 2

2. (a + 3) ^ 2

3. (x - 5) ^ 2

4. (x + 4) ^ 2

5. (a - 1/2) ^ 2

6. (x + 10) ^ 2

7. (x - 10) ^ 2

8. (a + 0.8) ^ 2

9. (2x - 1) ^ 2

10. (3x + 2) ^ 2

11. (3a + 5b) ^ 2

12. (5a - 3b) ^ 2

13. (2m - 7n) ^ 2

14. (x ^ 2 + 5) ^ 2

15. (a ^ 2 - 2) ^ 2

16. (x ^ 3 + 4) ^ 2

Let's apply the square of a binomial formula to each of these exercises.

### The formula to remember:
- For \((a + b)^2 = a^2 + 2ab + b^2\)
- For \((a - b)^2 = a^2 - 2ab + b^2\)

### Solutions:

1. **\((x - 2)^2\)**  
   \[
   x^2 - 2 \cdot x \cdot 2 + 2^2 = x^2 - 4x + 4
   \]

2. **\((a + 3)^2\)**  
   \[
   a^2 + 2 \cdot a \cdot 3 + 3^2 = a^2 + 6a + 9
   \]

3. **\((x - 5)^2\)**  
   \[
   x^2 - 2 \cdot x \cdot 5 + 5^2 = x^2 - 10x + 25
   \]

4. **\((x + 4)^2\)**  
   \[
   x^2 + 2 \cdot x \cdot 4 + 4^2 = x^2 + 8x + 16
   \]

5. **\((a - \frac{1}{2})^2\)**  
   \[
   a^2 - 2 \cdot a \cdot \frac{1}{2} + \left(\frac{1}{2}\right)^2 = a^2 - a + \frac{1}{4}
   \]

6. **\((x + 10)^2\)**  
   \[
   x^2 + 2 \cdot x \cdot 10 + 10^2 = x^2 + 20x + 100
   \]

7. **\((x - 10)^2\)**  
   \[
   x^2 - 2 \cdot x \cdot 10 + 10^2 = x^2 - 20x + 100
   \]

8. **\((a + 0.8)^2\)**  
   \[
   a^2 + 2 \cdot a \cdot 0.8 + 0.8^2 = a^2 + 1.6a + 0.64
   \]

9. **\((2x - 1)^2\)**  
   \[
   (2x)^2 - 2 \cdot 2x \cdot 1 + 1^2 = 4x^2 - 4x + 1
   \]

10. **\((3x + 2)^2\)**  
    \[
    (3x)^2 + 2 \cdot 3x \cdot 2 + 2^2 = 9x^2 + 12x + 4
    \]

11. **\((3a + 5b)^2\)**  
    \[
    (3a)^2 + 2 \cdot 3a \cdot 5b + (5b)^2 = 9a^2 + 30ab + 25b^2
    \]

12. **\((5a - 3b)^2\)**  
    \[
    (5a)^2 - 2 \cdot 5a \cdot 3b + (3b)^2 = 25a^2 - 30ab + 9b^2
    \]

13. **\((2m - 7n)^2\)**  
    \[
    (2m)^2 - 2 \cdot 2m \cdot 7n + (7n)^2 = 4m^2 - 28mn + 49n^2
    \]

14. **\((x^2 + 5)^2\)**  
    \[
    (x^2)^2 + 2 \cdot x^2 \cdot 5 + 5^2 = x^4 + 10x^2 + 25
    \]

15. **\((a^2 - 2)^2\)**  
    \[
    (a^2)^2 - 2 \cdot a^2 \cdot 2 + 2^2 = a^4 - 4a^2 + 4
    \]

16. **\((x^3 + 4)^2\)**  
    \[
    (x^3)^2 + 2 \cdot x^3 \cdot 4 + 4^2 = x^6 + 8x^3 + 16
    \]

Would you like to explore more examples or need any further explanation on any of the above steps?

### Related Questions:
1. How do you apply the square of a binomial to expressions with fractional coefficients?
2. What is the result when you expand \((2x + 3y)^2\)?
3. How can recognizing these patterns help when working with complex numbers?
4. Can you derive the general formula for \((a + b)^2\) from first principles?
5. How does the square of a binomial relate to the area of a geometric square?

**Tip:** When working with binomials, always remember the pattern \((a \pm b)^2 = a^2 \pm 2ab + b^2\); this can greatly speed up your calculations!

Explore and solve special product exercises in algebra, including (x - 2)^2, (a + 3)^2, and more. Learn the square of a binomial formula and its applications with detailed step-by-step solutions. Suitable for Grades 7-9 students.

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