Algebra practice exercise identifying parts of expressions.

Let’s go through each expression one by one and identify the Variables, Coefficients, Powers, and Constants.

Remember:
- A variable is a letter that stands for an unknown number (like x, y, m, etc.).
- A coefficient is the number multiplied by the variable. If there’s no number written, it’s 1 or -1.
- A power (or exponent) tells you how many times the variable is multiplied by itself. If no power is shown, it’s 1.
- A constant is a plain number with no variable attached.

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Expression 1: c

- Variable: c
- Coefficient: 1 (because “c” means “1×c”)
- Power: 1 (because “c” means “c¹”)
- Constant: none → leave blank

→ So:
Variables: c
Coefficients: 1 is coeff. of c
Powers: 1 is the power of c
Constant: (blank)

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Expression 2: y + 2

This has two parts: “y” and “+2”

- Variables: y
- Coefficients: 1 is coeff. of y (since “y” = “1y”)
- Powers: 1 is the power of y
- Constants: 2

→ So:
Variables: y
Coefficients: 1 is coeff. of y
Powers: 1 is the power of y
Constant: 2

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Expression 3: x² – 7

Two parts: “x²” and “–7”

- Variables: x
- Coefficients: 1 is coeff. of x (since “x²” = “1x²”)
- Powers: 2 is the power of x
- Constants: –7 (note: negative sign stays with the constant)

→ So:
Variables: x
Coefficients: 1 is coeff. of x
Powers: 2 is the power of x
Constant: –7

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Expression 4: 13 – 3m⁵

Two parts: “13” and “–3m⁵”

- Variables: m
- Coefficients: –3 is coeff. of m (the minus sign goes with the coefficient!)
- Powers: 5 is the power of m
- Constants: 13

→ So:
Variables: m
Coefficients: –3 is coeff. of m
Powers: 5 is the power of m
Constant: 13

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Expression 5: 4x + 5y⁻¹ – 12

Three parts: “4x”, “5y⁻¹”, “–12”

First term: 4x
→ Variable: x, Coeff: 4, Power: 1

Second term: 5y⁻¹
→ Variable: y, Coeff: 5, Power: –1 (yes, powers can be negative!)

Third term: –12 → constant

So we need to fill in both rows under this expression.

Row 1 (for 4x):
Variables: x
Coefficients: 4 is coeff. of x
Powers: 1 is the power of x

Row 2 (for 5y⁻¹):
Variables: y
Coefficients: 5 is coeff. of y
Powers: –1 is the power of y

Constant: –12

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Expression 6: 2a³b² – p⁻² + 4

Three parts: “2a³b²”, “–p⁻²”, “+4”

First term: 2a³b² → This has TWO variables: a and b
→ Coefficient: 2 (applies to both a and b together)
→ Power of a: 3
→ Power of b: 2

Second term: –p⁻² →
→ Variable: p
→ Coefficient: –1 (because “–p⁻²” = “–1 × p⁻²”)
→ Power: –2

Third term: +4 → constant

We have three lines to fill because there are three terms, but note: the first term has two variables — so we’ll list them separately? Wait — looking at the table structure, it seems they want us to break down each *term* into its components, even if multiple variables are in one term.

But the table only gives us 3 rows for this expression. Let’s see:

Actually, looking back at previous expressions like “4x + 5y⁻¹ – 12”, they used 2 rows for 2 variable terms and left constant separate. Here, we have:

Term 1: 2a³b² → involves two variables → maybe we treat as one term with two variables? But the table asks for “is coeff. of ___” and “is the power of ___” — implying per variable.

Wait — let’s check the original table again. For “4x + 5y⁻¹ – 12”, they gave two rows under coefficients/powers — meaning one row per variable term.

Similarly here, for “2a³b² – p⁻² + 4”, we have:

- First term: 2a³b² → this is ONE term with two variables. But since the table expects us to specify “is coeff. of [variable]” and “is the power of [variable]”, we probably need to split this into two entries? But the table only provides 3 rows total for this expression.

Looking at the layout:

For “2a³b² – p⁻² + 4”, there are 3 blank rows under it in the table. That matches the 3 terms:

Term 1: 2a³b² → but this has two variables. How to handle?

Actually, in algebra, when you have something like 2a³b², the coefficient is 2, and it applies to the whole product. The powers are 3 for a and 2 for b. Since the table has separate columns for “Variables”, “Coefficients”, “Powers”, and “Constant”, and for other multi-variable cases they didn’t appear yet — perhaps we should list each variable separately?

But wait — in the instruction, it says “Identify the following in each of the expressions below: Variables, Coefficients, Powers & Constant.”

And in the table, for “4x + 5y⁻¹ – 12”, they have two rows — one for x and one for y.

So likely, for “2a³b²”, we should make two rows: one for a and one for b.

But then we’d need 4 rows: a, b, p, and constant — but the table only gives 3 rows for this expression.

Hmm. Let me count the rows provided in the image for the last expression: yes, exactly 3 rows.

That suggests they consider “2a³b²” as one term, and we report:

In first row: for variable a → coeff 2, power 3
In second row: for variable b → coeff 2, power 2
In third row: for variable p → coeff –1, power –2
And constant 4 goes in the constant column.

But then what about the “is coeff. of” and “is the power of”? We can write:

Row 1:
Variables: a
Coefficients: 2 is coeff. of a
Powers: 3 is the power of a

Row 2:
Variables: b
Coefficients: 2 is coeff. of b
Powers: 2 is the power of b

Row 3:
Variables: p
Coefficients: –1 is coeff. of p
Powers: –2 is the power of p

Constant: 4

Yes, that fits the 3 rows and covers all variables.

Even though 2 is the coefficient for the whole term, it's still the coefficient for each variable within the term. In algebra, we say the coefficient of a in 2a³b² is 2b², but that’s more advanced. At this level, since they’re asking to identify parts simply, and given the pattern from earlier problems, I think they expect:

For 2a³b²:
- Coefficient for a is 2 (ignoring b for now)
- Power of a is 3
Similarly for b.

It’s a bit simplified, but matches the level of the worksheet.

Alternatively, maybe they want us to treat “2a³b²” as having coefficient 2, and then list both variables and their powers in the same row? But the table doesn’t allow that — each row has one “is coeff. of ___” and one “is the power of ___”.

Given the structure, I’ll go with splitting into two rows for a and b.

So final breakdown:

Expression: 2a³b² – p⁻² + 4

Row 1 (for a):
Variables: a
Coefficients: 2 is coeff. of a
Powers: 3 is the power of a

Row 2 (for b):
Variables: b
Coefficients: 2 is coeff. of b
Powers: 2 is the power of b

Row 3 (for p):
Variables: p
Coefficients: –1 is coeff. of p
Powers: –2 is the power of p

Constant: 4

Perfect — uses all 3 rows.

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Now, compiling all answers into the table format as requested.

Final Answer:

| Expression | Variables | Coefficients | Powers | Constant |
|-------------------|-----------|--------------------------|-------------------------|----------|
| c | c | 1 is coeff. of c | 1 is the power of c | |
| y + 2 | y | 1 is coeff. of y | 1 is the power of y | 2 |
| x² – 7 | x | 1 is coeff. of x | 2 is the power of x | –7 |
| 13 – 3m⁵ | m | –3 is coeff. of m | 5 is the power of m | 13 |
| 4x + 5y⁻¹ – 12 | x | 4 is coeff. of x | 1 is the power of x | –12 |
| | y | 5 is coeff. of y | –1 is the power of y | |
| 2a³b² – p⁻² + 4 | a | 2 is coeff. of a | 3 is the power of a | 4 |
| | b | 2 is coeff. of b | 2 is the power of b | |
| | p | –1 is coeff. of p | –2 is the power of p | |

Note: For expressions with multiple terms involving variables, we use multiple rows to list each variable separately, as shown in the example with "4x + 5y⁻¹ – 12". The constant is listed once per expression in the Constant column.