Question Combine like terms in expressions with variables and coefficients. $-7c + 2c - 3c - 5c =$ $3w + 4w^3 + 7w + w^2 - w^3 =$ $3a + 5b + a - (-2)b =$ $\frac{1}{2}v - \frac{2}{3}v + v =$

Studdy Solution

STEP 1

Assumptions1. We are combining like terms, which are terms that have the same variable and exponent. . The operation between the terms is either addition or subtraction.

STEP 2

For the first expression, identify the like terms.
$-7c,2c, -c, -5c$

STEP 3

Combine the like terms by adding or subtracting them.
$-7c +2c -3c -5c$

STEP 4

Calculate the combined value of the like terms.
$-7c +2c -3c -c = -13c$

STEP 5

For the second expression, identify the like terms.
$3w,7w$ $4w^3, -w^3$ $w^2$

STEP 6

Combine the like terms by adding or subtracting them.
$3w +w$ $4w^3 - w^3$ $w^2$

STEP 7

Calculate the combined value of the like terms.
$3w +7w =10w$ $4w^3 - w^3 =3w^3$ $w^2$

STEP 8

For the third expression, identify the like terms.
$3a, a$ $5b, -(-2)b$

STEP 9

Combine the like terms by adding or subtracting them.
$3a + a$ $5b - (-2b)$

STEP 10

Calculate the combined value of the like terms.
$3a + a =4a$ $5b - (-2b) =7b$

STEP 11

For the fourth expression, identify the like terms.
$\frac{}{}v, -\frac{}{3}v, v$

STEP 12

Combine the like terms by adding or subtracting them.
$\frac{}{2}v - \frac{2}{}v + v$

STEP 13

Calculate the combined value of the like terms.
$\frac{}{2}v - \frac{2}{3}v + v = \frac{5}{6}v$ So, the simplified expressions are $-13c$ $10w +3w^3 + w^2$ $a +7b$ $\frac{5}{6}v$

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Question Combine like terms in expressions with variables and coefficients. $-7c + 2c - 3c - 5c =$ $3w + 4w^3 + 7w + w^2 - w^3 =$ $3a + 5b + a - (-2)b =$ $\frac{1}{2}v - \frac{2}{3}v + v =$

Studdy Solution

STEP 1

Assumptions1. We are combining like terms, which are terms that have the same variable and exponent. . The operation between the terms is either addition or subtraction.

STEP 2

For the first expression, identify the like terms.
$-7c,2c, -c, -5c$

STEP 3

Combine the like terms by adding or subtracting them.
$-7c +2c -3c -5c$

STEP 4

Calculate the combined value of the like terms.
$-7c +2c -3c -c = -13c$

STEP 5

For the second expression, identify the like terms.
$3w,7w$ $4w^3, -w^3$ $w^2$

STEP 6

Combine the like terms by adding or subtracting them.
$3w +w$ $4w^3 - w^3$ $w^2$

STEP 7

Calculate the combined value of the like terms.
$3w +7w =10w$ $4w^3 - w^3 =3w^3$ $w^2$

STEP 8

For the third expression, identify the like terms.
$3a, a$ $5b, -(-2)b$

STEP 9

Combine the like terms by adding or subtracting them.
$3a + a$ $5b - (-2b)$

STEP 10

Calculate the combined value of the like terms.
$3a + a =4a$ $5b - (-2b) =7b$

STEP 11

For the fourth expression, identify the like terms.
$\frac{}{}v, -\frac{}{3}v, v$

STEP 12

Combine the like terms by adding or subtracting them.
$\frac{}{2}v - \frac{2}{}v + v$

STEP 13

Calculate the combined value of the like terms.
$\frac{}{2}v - \frac{2}{3}v + v = \frac{5}{6}v$ So, the simplified expressions are $-13c$ $10w +3w^3 + w^2$ $a +7b$ $\frac{5}{6}v$

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Studdy Solution

STEP 1

Assumptions1. We are combining like terms, which are terms that have the same variable and exponent. . The operation between the terms is either addition or subtraction.

STEP 2

For the first expression, identify the like terms.−7c,2c,−c,−5c-7c,2c, -c, -5c−7c,2c,−c,−5c

STEP 3

Combine the like terms by adding or subtracting them.−7c+2c−3c−5c-7c +2c -3c -5c−7c+2c−3c−5c

STEP 4

Calculate the combined value of the like terms.−7c+2c−3c−c=−13c-7c +2c -3c -c = -13c−7c+2c−3c−c=−13c

STEP 5

For the second expression, identify the like terms.3w,7w3w,7w3w,7w4w3,−w34w^3, -w^34w3,−w3w2w^2w2

STEP 6

Combine the like terms by adding or subtracting them.3w+w3w +w3w+w4w3−w34w^3 - w^34w3−w3w2w^2w2

STEP 7

Calculate the combined value of the like terms.3w+7w=10w3w +7w =10w3w+7w=10w4w3−w3=3w34w^3 - w^3 =3w^34w3−w3=3w3w2w^2w2

STEP 8

For the third expression, identify the like terms.3a,a3a, a3a,a5b,−(−2)b5b, -(-2)b5b,−(−2)b

STEP 9

Combine the like terms by adding or subtracting them.3a+a3a + a3a+a5b−(−2b)5b - (-2b)5b−(−2b)

STEP 10

Calculate the combined value of the like terms.3a+a=4a3a + a =4a3a+a=4a5b−(−2b)=7b5b - (-2b) =7b5b−(−2b)=7b

STEP 11

For the fourth expression, identify the like terms.v,−3v,v\frac{}{}v, -\frac{}{3}v, v​v,−3​v,v

STEP 12

Combine the like terms by adding or subtracting them.2v−2v+v\frac{}{2}v - \frac{2}{}v + v2​v−2​v+v

STEP 13

Calculate the combined value of the like terms.2v−23v+v=56v\frac{}{2}v - \frac{2}{3}v + v = \frac{5}{6}v2​v−32​v+v=65​vSo, the simplified expressions are−13c-13c−13c10w+3w3+w210w +3w^3 + w^210w+3w3+w2a+7ba +7ba+7b56v\frac{5}{6}v65​v

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For the first expression, identify the like terms.
$-7c,2c, -c, -5c$

Combine the like terms by adding or subtracting them.
$-7c +2c -3c -5c$

Calculate the combined value of the like terms.
$-7c +2c -3c -c = -13c$

For the second expression, identify the like terms.
$3w,7w$ $4w^3, -w^3$ $w^2$

Combine the like terms by adding or subtracting them.
$3w +w$ $4w^3 - w^3$ $w^2$

Calculate the combined value of the like terms.
$3w +7w =10w$ $4w^3 - w^3 =3w^3$ $w^2$

For the third expression, identify the like terms.
$3a, a$ $5b, -(-2)b$

Combine the like terms by adding or subtracting them.
$3a + a$ $5b - (-2b)$

Calculate the combined value of the like terms.
$3a + a =4a$ $5b - (-2b) =7b$

For the fourth expression, identify the like terms.
$\frac{}{}v, -\frac{}{3}v, v$

Combine the like terms by adding or subtracting them.
$\frac{}{2}v - \frac{2}{}v + v$

Calculate the combined value of the like terms.
$\frac{}{2}v - \frac{2}{3}v + v = \frac{5}{6}v$ So, the simplified expressions are $-13c$ $10w +3w^3 + w^2$ $a +7b$ $\frac{5}{6}v$