1

Problem

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

2

Step

The given expressions are

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

3

Step

Distribute negative to expression

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

4

Step

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

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

5

Step

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

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

6

Step

Combine like terms with q:

-3p - 4p = -7p

7

Step

Constant terms:

7 + 1 = 8

8

Step

Therefore, the simplified expression is:

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

9

Solution

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)\$.

10

Sumup

Please Summarize Problem, Hint, Clue, Formula and Steps

Choices

11

Choice-A

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

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

12

Choice-B

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

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

13

Choice-C

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

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

14

Choice-D

This option is correct as it accurately reflects the outcome of the subtraction operation

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

15

Step

Option

D

16

Sumup

Please Summarize Choices