Question

subtract the following polynomials: (7p + 4p³ - 8) - (-3p² + 2 - 9p) 4p³ +3p² +16p -10 3p³ + 4p² - p + 3 4p³ +3p² + 16p + 10 -3p² + 4p³ -15 + 9

Explanation:

Step1: Distribute the negative sign

To subtract the second polynomial, we distribute the negative sign to each term in \(-(-3p^{2}+2 - 9p)\). This gives us \(+ 3p^{2}-2 + 9p\). So the expression becomes:
\((7p + 4p^{3}-8)+3p^{2}-2 + 9p\)

Step2: Combine like terms

• For the \(p^{3}\) term: We have \(4p^{3}\) (only one term with \(p^{3}\)).
• For the \(p^{2}\) term: We have \(3p^{2}\) (only one term with \(p^{2}\)).
• For the \(p\) terms: Combine \(7p\) and \(9p\). \(7p+9p = 16p\).
• For the constant terms: Combine \(-8\) and \(-2\). \(-8-2=-10\).

Putting it all together, we get:
\(4p^{3}+3p^{2}+16p - 10\)

Answer:

\(4p^{3}+3p^{2}+16p - 10\) (which corresponds to the first option: \(4p^{3}+3p^{2}+16p - 10\))