Algebra worksheet explaining terms, constants, coefficients, and like terms with practice problems.

Let's solve each problem step by step using the vocabulary and concepts provided in the worksheet.

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Vocabulary Review:

- Term: One part of an algebraic expression (separated by + or – signs).
- Constant: A number without a variable.
- Coefficient: The number multiplying a variable.
- Like terms: Terms that have the same variable(s) raised to the same power (only differ in coefficients).

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Now, let’s go through each expression:

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1. $ 3 + 8x + 4 - 6x - 2 $

#### How many terms?
Break it down by + and – signs:
- $3$, $+8x$, $+4$, $-6x$, $-2$

So there are 5 terms.

#### What are the like terms?
Look for terms with the same variables:
- $8x$ and $-6x$ → both have $x$
- $3$, $4$, and $-2$ → all constants

So:
- Like terms: $8x$ and $-6x$; $3$, $4$, and $-2$

#### Which terms are constants?
Constants are numbers without variables:
- $3$, $4$, and $-2$

✔ Constants: 3, 4, -2

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2. $ x + x + y $

#### How many terms?
- $x$, $+x$, $+y$ → 3 terms

#### What are the like terms?
- $x$ and $x$ → same variable
- $y$ is different

So:
- Like terms: $x$ and $x$

#### Which terms are constants?
No term has no variable → none

✔ Constants: None

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3. $ 6 - 2x + 2 + 7x $

#### How many terms?
- $6$, $-2x$, $+2$, $+7x$ → 4 terms

#### What are the like terms?
- $-2x$ and $+7x$ → both have $x$
- $6$ and $2$ → both constants

So:
- Like terms: $-2x$ and $7x$; $6$ and $2$

#### Which terms are constants?
- $6$ and $2$ → no variables

✔ Constants: 6, 2

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4. $ 10a + 12 - 6 - 7a $

#### How many terms?
- $10a$, $+12$, $-6$, $-7a$ → 4 terms

#### What are the like terms?
- $10a$ and $-7a$ → both have $a$
- $12$ and $-6$ → both constants

So:
- Like terms: $10a$ and $-7a$; $12$ and $-6$

#### Which terms are constants?
- $12$ and $-6$ → no variables

✔ Constants: 12, -6

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✔ Final Answers:

#### 1. $ 3 + 8x + 4 - 6x - 2 $
- How many terms? → 5
- Like terms? → $8x$ and $-6x$; $3$, $4$, and $-2$
- Constants? → 3, 4, -2

#### 2. $ x + x + y $
- How many terms? → 3
- Like terms? → $x$ and $x$
- Constants? → None

#### 3. $ 6 - 2x + 2 + 7x $
- How many terms? → 4
- Like terms? → $-2x$ and $7x$; $6$ and $2$
- Constants? → 6, 2

#### 4. $ 10a + 12 - 6 - 7a $
- How many terms? → 4
- Like terms? → $10a$ and $-7a$; $12$ and $-6$
- Constants? → 12, -6

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