Question

Lani is solving the following polynomial, but Nate checks her work and tells her there is an error. What is the error?

(4x³ + 4x² - 8x) - (8x² - 16x + 4)

4x³ + 4x² - 8x - 8x² - 16x - 4

4x³ + 12x² - 24x - 4

Answer 1

The error in Lani's work is that she incorrectly subtracted the terms in the parentheses. The correct subtraction should be (4x³ + 4x² - 8x) - (8x² - 16x + 4) = 4x³ + 4x² - 8x - 8x² + 16x - 4. After rearranging and combining like terms, the simplified polynomial is 4x³ - 4x² + 8x - 4.

Step-by-step explanation:

The error in Lani's work is that she incorrectly subtracted the terms in the parentheses. When subtracting polynomials, it is important to distribute the negative sign to each term inside the parentheses.

The correct subtraction should be: (4x³ + 4x² - 8x) - (8x² - 16x + 4) = 4x³ + 4x² - 8x - 8x² + 16x - 4.

After rearranging and combining like terms, the simplified polynomial is: 4x³ - 4x² + 8x - 4.