Subtract \$(5p^3 + 2p^2 − 3p + 7)\$ and \$(2p^3 − p^2 + 4p − 1)\$.

The given expressions are

\$(5p^3 + 2p^2 − 3p + 7)\$, \$(2p^3 − p^2 + 4p − 1)\$

Distribute negative to expression

\$5p^3 + 2p^2 - 3p + 7 - 2p^3 + p^2 - 4p + 1\$

Combine like terms with \$q^3\$:

\$5p^3 - 2p^3 = 3p^3\$

Combine like terms with \$q^2\$:

\$2p^2 + p^2 = 3p^2\$

Combine like terms with q:

-3p - 4p = -7p

Constant terms:

7 + 1 = 8

Therefore, the simplified expression is:

\$3p^3 + 3p^2 - 7p + 8\$

So, \$3p^3 + 3p^2 - 7p + 8\$ is the simplified form of \$(5p^3 + 2p^2 − 3p + 7)\$ from \$(2p^3 − p^2 + 4p − 1)\$.

This option doesn’t match our calculated result, as it has incorrect coefficients and signs for some terms

\$ 7p^3 + 3p^2 - 7p - 8\$

Option B is inaccurate because of a sign mistake in its constant term

\$ 3p^3 + 3p^2 - 7p - 8\$

It does not match because it shows different coefficients for \$p^3\$ and \$p^2\$

\$ 7p^3 + 7p^2 - 7p + 8\$

Option D is correct as it accurately reflects the outcome of the subtraction operation

\$ 3p^3 + 3p^2 - 7p + 8\$

Option

D

Can you summarize what you’ve understood in the above steps?