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

Studdy Solution

STEP 1

Assumptions1. We are given two polynomial expressions $v^{4}+3 v-3 v^{}$ and $v^{4}-5 v^{}+5 v$ . We are asked to add these two expressions together.

STEP 2

To add these two expressions, we need to combine like terms. Like terms are terms that have the same variable and exponent.

STEP 3

First, we write down the given expressions one below the other, aligning like terms vertically.\begin{align} &2 v^{} -3 v^{2} +3 v \\ + & v^{} -5 v^{2} +5 v \\ \end{align}

STEP 4

Now, we add the coefficients of the like terms together.
\begin{align} & (2 v^{4} + v^{4}) + (-3 v^{2} - v^{2}) + (3 v + v) \\ \end{align}

STEP 5

Perform the addition to get the final expression.
\begin{align} & (2 +1) v^{4} + (-3 -5) v^{2} + (3 +5) v \\ \end{align}

STEP 6

implify the expression to obtain the final result.
\begin{align} &3 v^{4} -8 v^{2} +8 v \\ \end{align}
So, $\left(2 v^{4}+3 v-3 v^{2}\right)+\left(v^{4}-5 v^{2}+5 v\right) =3 v^{4} -8 v^{2} +8 v$ .

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

Studdy Solution

STEP 1

Assumptions1. We are given two polynomial expressions $v^{4}+3 v-3 v^{}$ and $v^{4}-5 v^{}+5 v$ . We are asked to add these two expressions together.

STEP 2

To add these two expressions, we need to combine like terms. Like terms are terms that have the same variable and exponent.

STEP 3

First, we write down the given expressions one below the other, aligning like terms vertically.\begin{align} &2 v^{} -3 v^{2} +3 v \\ + & v^{} -5 v^{2} +5 v \\ \end{align}

STEP 4

Now, we add the coefficients of the like terms together.
\begin{align} & (2 v^{4} + v^{4}) + (-3 v^{2} - v^{2}) + (3 v + v) \\ \end{align}

STEP 5

Perform the addition to get the final expression.
\begin{align} & (2 +1) v^{4} + (-3 -5) v^{2} + (3 +5) v \\ \end{align}

STEP 6

implify the expression to obtain the final result.
\begin{align} &3 v^{4} -8 v^{2} +8 v \\ \end{align}
So, $\left(2 v^{4}+3 v-3 v^{2}\right)+\left(v^{4}-5 v^{2}+5 v\right) =3 v^{4} -8 v^{2} +8 v$ .

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QuestionSimplify the expression: (2v4+3v−3v2)+(v4−5v2+5v)(2 v^{4}+3 v-3 v^{2})+(v^{4}-5 v^{2}+5 v)(2v4+3v−3v2)+(v4−5v2+5v).

Studdy Solution

STEP 1

Assumptions1. We are given two polynomial expressions v4+3v−3v v^{4}+3 v-3 v^{}v4+3v−3v and v4−5v+5vv^{4}-5 v^{}+5 vv4−5v+5v . We are asked to add these two expressions together.

STEP 2

To add these two expressions, we need to combine like terms. Like terms are terms that have the same variable and exponent.

STEP 3

First, we write down the given expressions one below the other, aligning like terms vertically.\begin{align*} &2 v^{} -3 v^{2} +3 v \\ + & v^{} -5 v^{2} +5 v \\ \end{align*}

STEP 4

Now, we add the coefficients of the like terms together.\begin{align*} & (2 v^{4} + v^{4}) + (-3 v^{2} - v^{2}) + (3 v + v) \\ \end{align*}

STEP 5

Perform the addition to get the final expression.\begin{align*} & (2 +1) v^{4} + (-3 -5) v^{2} + (3 +5) v \\ \end{align*}

STEP 6

implify the expression to obtain the final result.\begin{align*} &3 v^{4} -8 v^{2} +8 v \\ \end{align*}So, (2v4+3v−3v2)+(v4−5v2+5v)=3v4−8v2+8v\left(2 v^{4}+3 v-3 v^{2}\right)+\left(v^{4}-5 v^{2}+5 v\right) =3 v^{4} -8 v^{2} +8 v(2v4+3v−3v2)+(v4−5v2+5v)=3v4−8v2+8v.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

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

Assumptions1. We are given two polynomial expressions $v^{4}+3 v-3 v^{}$ and $v^{4}-5 v^{}+5 v$ . We are asked to add these two expressions together.

First, we write down the given expressions one below the other, aligning like terms vertically.\begin{align} &2 v^{} -3 v^{2} +3 v \\ + & v^{} -5 v^{2} +5 v \\ \end{align}

Now, we add the coefficients of the like terms together.
\begin{align} & (2 v^{4} + v^{4}) + (-3 v^{2} - v^{2}) + (3 v + v) \\ \end{align}

Perform the addition to get the final expression.
\begin{align} & (2 +1) v^{4} + (-3 -5) v^{2} + (3 +5) v \\ \end{align}

implify the expression to obtain the final result.
\begin{align} &3 v^{4} -8 v^{2} +8 v \\ \end{align}
So, $\left(2 v^{4}+3 v-3 v^{2}\right)+\left(v^{4}-5 v^{2}+5 v\right) =3 v^{4} -8 v^{2} +8 v$ .