Question

(-9n⁴ + 8) - (-9n⁴ + 2n³ + 5n²) = 2n³ + 5n² - 8

Options:
a) -2n³ - 5n² + 8
b) 2n³ + 5n² - 8
c) -2n³ - 5n² - 8
d) 2n³ - 5n² + 8

Answer 1

To simplify the given expression, distribute the subtraction sign, combine like terms, and simplify to get -2n³ - 5n² + 8 as the correct answer.

Step-by-step explanation:

The question requires simplifying the expression (-9n⁴ + 8) - (-9n⁴ + 2n³ + 5n²). To simplify, you distribute the subtraction sign across the terms in the second set of parentheses, which will change the signs of the terms inside those parentheses. This yields the following steps:

• Remove parentheses: -9n⁴ + 8 + 9n⁴ - 2n³ - 5n²
• Combine like terms: -9n⁴ cancels with +9n⁴, and you're left with -2n³ - 5n² + 8.

Thus, the correct answer is (b) -2n³ - 5n² + 8.