Question

1. subtract (dont forget to distribute -1 to one equation):

(-12x⁴ + 7x³) - (x³ + 2x⁴)

Explanation:

Step1: Distribute -1 to the second polynomial

To subtract the second polynomial from the first, we distribute the -1 to each term inside the parentheses: \((-12x^{4}+7x^{3}) - x^{3}-2x^{4}\)

Step2: Combine like terms for \(x^{4}\) terms

The \(x^{4}\) terms are \(-12x^{4}\) and \(-2x^{4}\). Combining them: \(-12x^{4}-2x^{4} = -14x^{4}\)

Step3: Combine like terms for \(x^{3}\) terms

The \(x^{3}\) terms are \(7x^{3}\) and \(-x^{3}\). Combining them: \(7x^{3}-x^{3}=6x^{3}\)

Step4: Write the final result

Putting the combined terms together, we get \(-14x^{4}+6x^{3}\)

Answer:

\(-14x^{4} + 6x^{3}\)