Expand and evaluate

Part 3: Expand the following expressions. Answers may vary.

Part 4: Write the following expressions in standard form.

Part 5: Color the box with the term that does not belong to the group.

a. −ퟑ풂풃풄

풂풃풄

풂

ퟐ

풃풄

ퟏퟎ풂풃풄

ퟏퟎퟎ풂풃풄

b.   ퟓ풎

ퟑ

풏

ퟐ

−풎

ퟑ

풏

ퟐ

ퟖ풎

ퟑ

풏

ퟐ

ퟏퟔ풎

ퟑ

풏

ퟐ

−ퟒퟓ풎

ퟑ

풏

ퟑ

a.

ퟏퟐ

ퟑ

Let's break this down and solve each part in sequence.

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### **Part 3: Expand the following expressions.**

Since no specific expressions are given for expansion in Part 3, let's assume you will input those for me later. Expansion typically involves distributing terms and combining like terms.

---

### **Part 4: Write the following expressions in standard form.**

For the expressions in this section, we aim to write each term in standard form. **Standard form** for an expression generally means:

- All terms arranged in decreasing order of exponents (or alphabetical order in terms of variables).
- Simplified, with like terms combined.

---

### **Part 5: Color the box with the term that does not belong to the group.**

We need to identify which term in each list is different from the others, typically based on patterns like missing variables or differences in degree.

---

#### **a. Group:**
1. \( -3abc \)
2. \( abc \)
3. \( a \)
4. \( 2 \)
5. \( bc \)
6. \( 10abc \)
7. \( 100abc \)

The term that does not belong to the group is **\( 2 \)**.

- Reason: All other terms contain variables like \(a\), \(b\), or \(c\), but \(2\) is just a constant without any variables.

---

#### **b. Group:**
1. \( 5m^3n^2 \)
2. \( 3n^2 \)
3. \( -m^3n^2 \)
4. \( 8m^3n^2 \)
5. \( 16m^3n^2 \)
6. \( -45m^3n^3 \)

The term that does not belong to the group is **\( -45m^3n^3 \)**.

- Reason: All other terms have an exponent of 2 on \(n\), while this term has \(n^3\), making it different in degree.

---

#### **c. Group:**
1. \( \frac{12}{3} \) simplifies to **4**.

There's only one term here, so no further evaluation is needed.

---

Would you like further details or explanations for any of the parts? Here are some follow-up questions for deeper understanding:

---

### Follow-up questions:

1. Can you input the expressions for Part 3 so I can help expand them?
2. In Part 4, do you have specific expressions you'd like to see written in standard form?
3. Would you like to explore more examples of terms that don't belong in different groups?
4. Should I explain more about how I identified the "odd" term in Part 5?
5. Would you like to see how these concepts apply to more complex algebraic structures?

### Tip:
When identifying terms that don't belong in a group, focus on comparing factors like exponents, variable presence, and whether the term is a constant or involves variables.

Expand and evaluate Part 3: Expand the following expressions. Answers may vary. Part 4: Write the following expressions in standard form. Part 5: Color the box with the term that does not belong to the group. a. −3abc, abc, a, 2, bc, 10abc, 100abc b. 5m^3n^2, 3n^2, −m^3n^2, 8m^3n^2, 16m^3n^2, −45m^3n^3 a. 12/3

Learn how to expand algebraic expressions, write them in standard form, and identify the term that doesn't belong in a group. This problem covers key algebraic concepts suitable for Grades 6-8, including expansion using the distributive property and evaluating standard form.

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