QuestionSimplify the expression: $(6 p^{3}-p+6 p^{4})+(8 p-5 p^{4}+2 p^{3})$ .

Studdy Solution

STEP 1

Assumptions1. The problem involves adding two polynomial expressions. . The polynomials are in the form of $ax^n$ , where $a$ is the coefficient, $x$ is the variable, and $n$ is the degree of the term.
3. The like terms in the polynomials can be combined. Like terms are terms that have the same variable and exponent.

STEP 2

First, let's write down the given problem.
$\left(6 p^{}-p+6 p^{4}\right)+\left(8 p-5 p^{4}+2 p^{}\right)$

STEP 3

Remove the parentheses. Since there are no negative signs in front of the parentheses, we can simply remove them without changing the signs of the terms inside.
$6 p^{3}-p+6 p^{}+8 p-5 p^{}+2 p^{3}$

STEP 4

Now, we can combine like terms. The like terms are $6p^4$ and $-p^4$ , $6p^3$ and $2p^3$ , and $-p$ and $8p$ .
$\left(6 p^{4}- p^{4}\right)+\left(6 p^{3}+2 p^{3}\right)+\left(-p+8 p\right)$

STEP 5

Perform the addition and subtraction for each set of like terms.
$p^{4}+8 p^{3}+7 p$ So, the simplified form of the given expression is $p^{4}+8 p^{3}+7 p$ .

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