Final answer:
To simplify the expression 8i(8b-7i)+4b(4b-5i), distribute and combine like terms to get 320b - 36i.
Step-by-step explanation:
To simplify the expression 8i(8b-7i)+4b(4b-5i), distribute the values within each set of parentheses:
First expression: 8i * 8b - 8i * 7i
Second expression: 4b * 4b - 4b * 5i
Combine like terms:
64bi - 56i² + 16b² - 20bi
Combine like terms again:
(16b² - 20bi) + (64bi - 56i²)
Finally, simplify and rearrange the terms:
16b² + 44bi - 56i²
In the form a + bi, the simplified expression is 16b² - 56i² + 44bi. Since i² is equal to -1, the expression can be further simplified to 16b² + 56 + 44bi. Therefore, the correct answer is 320b - 36i (option b).