Let's work through each problem in the image step-by-step.

Question 17

$7.50 \times \left( \frac{4}{10} + 16\% \right) \times 8.27 = \, ?$

1. Calculate $\frac{4}{10} = 0.4$.
2. $16\%$ as a decimal is $0.16$.
3. Sum the values: $0.4 + 0.16 = 0.56$.
4. Multiply: $7.50 \times 0.56 \times 8.27$.

Calculating:

$7.50 \times 0.56 = 4.20$ $4.20 \times 8.27 = 34.374$

Answer: $34.374$.

Question 18

$56.34^2 - 43.66^2 = \, ?$

This is a difference of squares formula: $(a^2 - b^2 = (a-b)(a+b))$.

1. Calculate $56.34 - 43.66 = 12.68$.
2. Calculate $56.34 + 43.66 = 100$.
3. Multiply: $12.68 \times 100 = 1268$.

Answer: $1268$.

Question 19

$2 + \frac{1}{5} - \frac{2}{3} \times \frac{3}{7} = \, ?$

1. Calculate the multiplication first: $\frac{2}{3} \times \frac{3}{7} = \frac{6}{21} = \frac{2}{7}$.
2. Now we have $2 + \frac{1}{5} - \frac{2}{7}$.
3. Find a common denominator for $\frac{1}{5}$ and $\frac{2}{7}$: $35$. $\frac{1}{5} = \frac{7}{35}, \quad \frac{2}{7} = \frac{10}{35}$
4. Calculate: $2 + \frac{7}{35} - \frac{10}{35} = 2 - \frac{3}{35} = \frac{67}{35}$.

Answer: $\frac{67}{35}$.

Question 20

$12^2 - 70 + 2 \times 13 = \, ?$

1. Calculate $12^2 = 144$.
2. Calculate $2 \times 13 = 26$.
3. Substitute: $144 - 70 + 26$.
4. Calculate: $144 - 70 = 74$.
5. $74 + 26 = 100$.

Answer: $100$.

Question 21

$2024^2 - 2020 \times 2028 = \, ?$

1. Use the identity $(a - b)(a + b) = a^2 - b^2$, where $a = 2024$ and $b = 2022$.
2. Calculate: $2024^2 - 2020 \times 2028 = (2024 - 2020)(2024 + 2020)$.
3. $2024 - 2020 = 4$.
4. $2024 + 2020 = 4044$.
5. Multiply: $4 \times 4044 = 16176$.

Answer: $16176$.

Let me know which question you'd like to discuss further or if there are any adjustments you'd like. Here are five related problems:

1. Simplify $(\frac{3}{7} + \frac{2}{5}) \times 8.5$.
2. Calculate $25.36^2 - 12.12^2$.
3. Evaluate $2x^2 - 5x + 3$ for $x = 4$.
4. Simplify $\frac{3}{8} + \frac{2}{9}$.
5. Find $24^2 - 13 \times 2 + 5$.

Tip: When solving algebraic problems, always prioritize parentheses and exponents before performing multiplication and addition.