If a * b = a² + b² - ab, then the value of 8 * 7 - 3 * 5 is:

Q: If a * b = a² + b² - ab, then the value of 8 * 7 - 3 * 5 is:

To solve the problem, we need to evaluate the expression $8 * 7 - 3 * 5$ using the operation defined as $a * b = a^2 + b^2 - ab$. First, let's calculate $8 * 7$: \[ 8 * 7 = 8^2 + 7^2 - 8 \times 7 \] Calculating each term: - $8^2 = 64$ - $7^2 = 49$ - $8 \times 7 = 56$ Substituting these values into the expression: \[ 8 * 7 = 64 + 49 - 56 = 113 - 56 = 57 \] Next, calculate $3 * 5$: \[ 3 * 5 = 3^2 + 5^2 - 3 \times 5 \] Calculating each term: - $3^2 = 9$ - $5^2 = 25$ - $3 \times 5 = 15$ Substituting these values into the expression: \[ 3 * 5 = 9 + 25 - 15 = 34 - 15 = 19 \] Now, substitute these results back into the original expression: \[ 8 * 7 - 3 * 5 = 57 - 19 = 38 \] Therefore, the value of $8 * 7 - 3 * 5$ is 38, which corresponds to Option 4. ### Explanation of Why Each Option is Incorrect: 1. **Option 1 (41):** This option is incorrect because the calculated result of $8 * 7 - 3 * 5$ is 38, not 41. The calculations for each operation were verified step-by-step, and 41 does not match the final result. 2. **Option 2 (58):** This option is incorrect because the correct calculation of the expression yields 38. The operations were performed accurately, and 58 does not align with the computed value. 3. **Option 3 (64):** This option is incorrect because the final result of the expression is 38. The calculations were checked thoroughly, and 64 is not the correct outcome. 4. **Option 4 (38):** This is the correct option, as demonstrated by the detailed calculations above. The operations were performed according to the given definition, and the result matches the expected value of 38. In conclusion, Option 4 is the correct answer, as the calculations confirm that the value of $8 * 7 - 3 * 5$ is indeed 38.

Question

Accepted Answer

To solve the problem, we need to evaluate the expression $8 * 7 - 3 * 5$ using the operation defined as $a * b = a^2 + b^2 - ab$.

First, let's calculate $8 * 7$:

$$
8 * 7 = 8^2 + 7^2 - 8 \times 7
$$

Calculating each term:

- $8^2 = 64$
- $7^2 = 49$
- $8 \times 7 = 56$

Substituting these values into the expression:

$$
8 * 7 = 64 + 49 - 56 = 113 - 56 = 57
$$

Next, calculate $3 * 5$:

$$
3 * 5 = 3^2 + 5^2 - 3 \times 5
$$

Calculating each term:

- $3^2 = 9$
- $5^2 = 25$
- $3 \times 5 = 15$

Substituting these values into the expression:

$$
3 * 5 = 9 + 25 - 15 = 34 - 15 = 19
$$

Now, substitute these results back into the original expression:

$$
8 * 7 - 3 * 5 = 57 - 19 = 38
$$

Therefore, the value of $8 * 7 - 3 * 5$ is 38, which corresponds to Option 4.

### Explanation of Why Each Option is Incorrect:

1. **Option 1 (41):** This option is incorrect because the calculated result of $8 * 7 - 3 * 5$ is 38, not 41. The calculations for each operation were verified step-by-step, and 41 does not match the final result.

2. **Option 2 (58):** This option is incorrect because the correct calculation of the expression yields 38. The operations were performed accurately, and 58 does not align with the computed value.

3. **Option 3 (64):** This option is incorrect because the final result of the expression is 38. The calculations were checked thoroughly, and 64 is not the correct outcome.

4. **Option 4 (38):** This is the correct option, as demonstrated by the detailed calculations above. The operations were performed according to the given definition, and the result matches the expected value of 38.

In conclusion, Option 4 is the correct answer, as the calculations confirm that the value of $8 * 7 - 3 * 5$ is indeed 38.