Question

Written as a simplified polynomial in standard form, what is the result when (x+8)² (x+8) 2 is subtracted from 4x²+54x²+5?

Answer 1

To find the simplified polynomial in standard form, combine like terms of 4x² + 54x² + 5 to get 58x² + 5, expand (x+8) to the third power, subtract the result from the first polynomial, and finally combine like terms to get the simplified form: -x³ + 34x² - 192x - 507.

Step-by-step explanation:

The task is to subtract the square of the binomial (x+8)² multiplied by (x+8) from the polynomial 4x² + 54x² + 5, and then to express the result in simplified standard form. First, we need to simplify the given expression:

1. Simplify the polynomial 4x² + 54x² + 5 by combining like terms:
58x² + 5

2. Expand the binomial (x+8)² to get x² + 16x + 64, then multiply this by (x+8) to get:
(x² + 16x + 64)(x + 8) which expands to x³ + 24x² + 192x + 512

3. Subtract the expanded cubic polynomial from the simplified polynomial:
58x² + 5 - (x³ + 24x² + 192x + 512)

4. Combine like terms to get the result in simplified standard form:
-x³ + 34x² - 192x - 507