Math

QuestionSimplify the expression: (5n35n26n4)+(7n4+n24n)\left(5 n^{3}-5 n^{2}-6 n^{4}\right)+\left(7 n^{4}+n^{2}-4 n\right).

Studdy Solution

STEP 1

Assumptions1. We are given two polynomial expressions and we need to add them. . The variable in both expressions is nn.

STEP 2

The first step in adding these two polynomial expressions is to identify like terms. Like terms are terms that have the same variable raised to the same power.The like terms in the given expressions are n4n^{4}, nn^{}, n2n^{2}, and nn.

STEP 3

The next step is to add the coefficients of the like terms. The coefficient of a term is the number in front of the variable.For the nn^{} terms, we have 6n-6n^{} and 7n7n^{}.

STEP 4

Add the coefficients of the n4n^{4} terms.
6n4+7n4=n4-6n^{4} +7n^{4} = n^{4}

STEP 5

For the n3n^{3} term, we only have 5n35n^{3} in the first expression.

STEP 6

Since there is no n3n^{3} term in the second expression, the n3n^{3} term in the sum will be 5n35n^{3}.

STEP 7

For the n2n^{2} terms, we have 5n2-5n^{2} and n2n^{2}.

STEP 8

Add the coefficients of the n2n^{2} terms.
5n2+n2=4n2-5n^{2} + n^{2} = -4n^{2}

STEP 9

For the nn terms, we have 4n-4n in the second expression.

STEP 10

Since there is no nn term in the first expression, the nn term in the sum will be 4n-4n.

STEP 11

Now, we combine all the terms we found to form the sum of the two given expressions.
n4+5n34n4nn^{4} +5n^{3} -4n^{} -4nSo, (5n35n6n4)+(7n4+n4n)=n4+5n34n4n\left(5 n^{3}-5 n^{}-6 n^{4}\right)+\left(7 n^{4}+n^{}-4 n\right) = n^{4} +5n^{3} -4n^{} -4n.

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