$ ext{If } a * b = a + b + ab, ext{ then the value of } 8 * 7 - 5 * 6 ext{ is:}$

Q: $\text{If } a * b = a + b + ab, \text{ then the value of } 8 * 7 - 5 * 6 \text{ is:}$

To solve the problem, we need to evaluate the expression $8 * 7 - 5 * 6$ using the given operation $a * b = a + b + ab$. 1. **Calculate $8 * 7$:** Using the operation $a * b = a + b + ab$, substitute $a = 8$ and $b = 7$: \[ 8 * 7 = 8 + 7 + (8 \times 7) \] \[ = 8 + 7 + 56 \] \[ = 71 \] 2. **Calculate $5 * 6$:** Again, using the operation $a * b = a + b + ab$, substitute $a = 5$ and $b = 6$: \[ 5 * 6 = 5 + 6 + (5 \times 6) \] \[ = 5 + 6 + 30 \] \[ = 41 \] 3. **Evaluate the expression $8 * 7 - 5 * 6$:** Substitute the values we calculated: \[ 8 * 7 - 5 * 6 = 71 - 41 \] \[ = 30 \] The correct answer is Option 1: 30. **Explanation of Options:** - **Option 1 (56):** This option is incorrect because the correct calculation of $8 * 7 - 5 * 6$ results in 30, not 56. - **Option 2 (45):** This option is incorrect because the correct calculation results in 30, not 45. - **Option 3 (40):** This option is incorrect because the correct calculation results in 30, not 40. - **Option 4 (30):** This option is correct because the calculation $8 * 7 - 5 * 6$ indeed results in 30. Therefore, the correct answer is Option 4: 30.

Question

$	ext{If } a * b = a + b + ab, 	ext{ then the value of } 8 * 7 - 5 * 6 	ext{ is:}$

Accepted Answer

To solve the problem, we need to evaluate the expression $8 * 7 - 5 * 6$ using the given operation $a * b = a + b + ab$.

1. **Calculate $8 * 7$:**

Using the operation $a * b = a + b + ab$, substitute $a = 8$ and $b = 7$:

$$
   8 * 7 = 8 + 7 + (8 \times 7)
   $$

$$
   = 8 + 7 + 56
   $$

$$
   = 71
   $$

2. **Calculate $5 * 6$:**

Again, using the operation $a * b = a + b + ab$, substitute $a = 5$ and $b = 6$:

$$
   5 * 6 = 5 + 6 + (5 \times 6)
   $$

$$
   = 5 + 6 + 30
   $$

$$
   = 41
   $$

3. **Evaluate the expression $8 * 7 - 5 * 6$:**

Substitute the values we calculated:

$$
   8 * 7 - 5 * 6 = 71 - 41
   $$

$$
   = 30
   $$

The correct answer is Option 1: 30.

**Explanation of Options:**

- **Option 1 (56):** This option is incorrect because the correct calculation of $8 * 7 - 5 * 6$ results in 30, not 56.

- **Option 2 (45):** This option is incorrect because the correct calculation results in 30, not 45.

- **Option 3 (40):** This option is incorrect because the correct calculation results in 30, not 40.

- **Option 4 (30):** This option is correct because the calculation $8 * 7 - 5 * 6$ indeed results in 30.

Therefore, the correct answer is Option 4: 30.