Question Subtract and simplify the polynomials: $\left(\frac{2}{7} p^{2}-\frac{1}{2} p q+\frac{3}{14} q^{2}+14\right)-\left(\frac{9}{14} p^{2}+\frac{4}{7} p q-\frac{5}{14} q^{2}+11\right)$ .

Studdy Solution

STEP 1

Assumptions1. We are given two polynomials. We need to subtract the second polynomial from the first one3. We need to simplify the result

STEP 2

We can rewrite the subtraction of the two polynomials as the addition of the first polynomial and the negation of the second polynomial.
$\left(\frac{2}{7} p^{2}-\frac{1}{2} p q+\frac{}{14} q^{2}+14\right)+\left(-\frac{9}{14} p^{2}-\frac{4}{7} p q+\frac{5}{14} q^{2}-11\right)$

STEP 3

Now, we can combine like terms. We start by combining the $p^{2}$ terms.
$\left(\frac{2}{7}-\frac{9}{14}\right) p^{2}$

STEP 4

Calculate the coefficient for the $p^{2}$ term.
$\left(\frac{2}{7}-\frac{9}{14}\right) = -\frac{}{14}$ So, the $p^{2}$ term after subtraction is $-\frac{}{14} p^{2}$ .

STEP 5

Next, we combine the $pq$ terms.
$\left(-\frac{1}{2}-\frac{4}{7}\right) p q$

STEP 6

Calculate the coefficient for the $pq$ term.
$\left(-\frac{1}{2}-\frac{4}{}\right) = -\frac{15}{14}$ So, the $pq$ term after subtraction is $-\frac{15}{14} pq$ .

STEP 7

Next, we combine the $q^{2}$ terms.
$\left(\frac{3}{14}+\frac{5}{14}\right) q^{2}$

STEP 8

Calculate the coefficient for the $q^{2}$ term.
$\left(\frac{3}{14}+\frac{5}{14}\right) = \frac{8}{14}$ So, the $q^{2}$ term after subtraction is $\frac{8}{14} q^{2}$ .

STEP 9

Finally, we combine the constant terms.
$\left(14-11\right)$

STEP 10

Calculate the constant term after subtraction.
$\left(14-\right) =3$

STEP 11

Now, we can write down the final result by combining all the terms we calculated.
$-\frac{5}{14} p^{} -\frac{15}{14} pq + \frac{8}{14} q^{} +3$ So, the subtraction of the given polynomials simplifies to $-\frac{5}{14} p^{} -\frac{15}{14} pq + \frac{8}{14} q^{} +3$ .

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Question Subtract and simplify the polynomials: $\left(\frac{2}{7} p^{2}-\frac{1}{2} p q+\frac{3}{14} q^{2}+14\right)-\left(\frac{9}{14} p^{2}+\frac{4}{7} p q-\frac{5}{14} q^{2}+11\right)$ .

Studdy Solution

STEP 1

Assumptions1. We are given two polynomials. We need to subtract the second polynomial from the first one3. We need to simplify the result

STEP 2

We can rewrite the subtraction of the two polynomials as the addition of the first polynomial and the negation of the second polynomial.
$\left(\frac{2}{7} p^{2}-\frac{1}{2} p q+\frac{}{14} q^{2}+14\right)+\left(-\frac{9}{14} p^{2}-\frac{4}{7} p q+\frac{5}{14} q^{2}-11\right)$

STEP 3

Now, we can combine like terms. We start by combining the $p^{2}$ terms.
$\left(\frac{2}{7}-\frac{9}{14}\right) p^{2}$

STEP 4

Calculate the coefficient for the $p^{2}$ term.
$\left(\frac{2}{7}-\frac{9}{14}\right) = -\frac{}{14}$ So, the $p^{2}$ term after subtraction is $-\frac{}{14} p^{2}$ .

STEP 5

Next, we combine the $pq$ terms.
$\left(-\frac{1}{2}-\frac{4}{7}\right) p q$

STEP 6

Calculate the coefficient for the $pq$ term.
$\left(-\frac{1}{2}-\frac{4}{}\right) = -\frac{15}{14}$ So, the $pq$ term after subtraction is $-\frac{15}{14} pq$ .

STEP 7

Next, we combine the $q^{2}$ terms.
$\left(\frac{3}{14}+\frac{5}{14}\right) q^{2}$

STEP 8

Calculate the coefficient for the $q^{2}$ term.
$\left(\frac{3}{14}+\frac{5}{14}\right) = \frac{8}{14}$ So, the $q^{2}$ term after subtraction is $\frac{8}{14} q^{2}$ .

STEP 9

Finally, we combine the constant terms.
$\left(14-11\right)$

STEP 10

Calculate the constant term after subtraction.
$\left(14-\right) =3$

STEP 11

Now, we can write down the final result by combining all the terms we calculated.
$-\frac{5}{14} p^{} -\frac{15}{14} pq + \frac{8}{14} q^{} +3$ So, the subtraction of the given polynomials simplifies to $-\frac{5}{14} p^{} -\frac{15}{14} pq + \frac{8}{14} q^{} +3$ .

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Studdy Solution

STEP 1

Assumptions1. We are given two polynomials. We need to subtract the second polynomial from the first one3. We need to simplify the result

STEP 2

STEP 3

Now, we can combine like terms. We start by combining the p2p^{2}p2 terms.(27−914)p2\left(\frac{2}{7}-\frac{9}{14}\right) p^{2} (72​−149​)p2

STEP 4

Calculate the coefficient for the p2p^{2}p2 term.(27−914)=−14\left(\frac{2}{7}-\frac{9}{14}\right) = -\frac{}{14} (72​−149​)=−14​So, the p2p^{2}p2 term after subtraction is −14p2-\frac{}{14} p^{2}−14​p2.

STEP 5

Next, we combine the pqpqpq terms.(−12−47)pq\left(-\frac{1}{2}-\frac{4}{7}\right) p q(−21​−74​)pq

STEP 6

Calculate the coefficient for the pqpqpq term.(−12−4)=−1514\left(-\frac{1}{2}-\frac{4}{}\right) = -\frac{15}{14} (−21​−4​)=−1415​So, the pqpqpq term after subtraction is −1514pq-\frac{15}{14} pq−1415​pq.

STEP 7

Next, we combine the q2q^{2}q2 terms.(314+514)q2\left(\frac{3}{14}+\frac{5}{14}\right) q^{2} (143​+145​)q2

STEP 8

Calculate the coefficient for the q2q^{2}q2 term.(314+514)=814\left(\frac{3}{14}+\frac{5}{14}\right) = \frac{8}{14} (143​+145​)=148​So, the q2q^{2}q2 term after subtraction is 814q2\frac{8}{14} q^{2}148​q2.

STEP 9

Finally, we combine the constant terms.(14−11)\left(14-11\right) (14−11)

STEP 10

Calculate the constant term after subtraction.(14−)=3\left(14-\right) =3(14−)=3

STEP 11

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Now, we can combine like terms. We start by combining the $p^{2}$ terms.
$\left(\frac{2}{7}-\frac{9}{14}\right) p^{2}$

Calculate the coefficient for the $p^{2}$ term.
$\left(\frac{2}{7}-\frac{9}{14}\right) = -\frac{}{14}$ So, the $p^{2}$ term after subtraction is $-\frac{}{14} p^{2}$ .

Next, we combine the $pq$ terms.
$\left(-\frac{1}{2}-\frac{4}{7}\right) p q$

Calculate the coefficient for the $pq$ term.
$\left(-\frac{1}{2}-\frac{4}{}\right) = -\frac{15}{14}$ So, the $pq$ term after subtraction is $-\frac{15}{14} pq$ .

Next, we combine the $q^{2}$ terms.
$\left(\frac{3}{14}+\frac{5}{14}\right) q^{2}$

Calculate the coefficient for the $q^{2}$ term.
$\left(\frac{3}{14}+\frac{5}{14}\right) = \frac{8}{14}$ So, the $q^{2}$ term after subtraction is $\frac{8}{14} q^{2}$ .

Finally, we combine the constant terms.
$\left(14-11\right)$

Calculate the constant term after subtraction.
$\left(14-\right) =3$