Question

Perform the indicated operation. (2a² - 8)(4a⁴ + 16a² + 64)

Answer 1

The operation (2a² - 8)(4a⁴ + 16a² + 64) simplifies to 8a⁶ - 512 after distributing and combining like terms.

Step-by-step explanation:

The student asked to perform the indicated operation: (2a² - 8)(4a⁴ + 16a² + 64). This question requires us to multiply two polynomials. To do this, we will use the distributive property, sometimes known as the FOIL method when dealing with binomials.

First, we multiply each term in the first polynomial by each term in the second polynomial and then combine like terms. It will look like this:

• (2a²) * (4a⁴) = 8a⁶
• (2a²) * (16a²) = 32a⁴
• (2a²) * (64) = 128a²
• (-8) * (4a⁴) = -32a⁴
• (-8) * (16a²) = -128a²
• (-8) * (64) = -512

Now we add the like terms together:

1. 8a⁶ + (32a⁴ - 32a⁴) + (128a² - 128a²) - 512
2. Since 32a⁴ - 32a⁴ = 0 and 128a² - 128a² = 0, these terms cancel each other out.
3. The final answer is 8a⁶ - 512.