Adding Like Terms

To add like terms, add the coefficients and keep the variable the same.

Example: Simplify $6n + n + 2n$

Solution: $6n + n + 2n = (6 + 1 + 2)n = 9n$

Subtracting Like Terms

To subtract like terms, subtract the coefficients and keep the variable the same.

Example: Simplify $7mk - 4mk - mk$

Solution: $7mk - 4mk - mk = (7 - 4 - 1)mk = 2mk$

Combining Addition and Subtraction

When an expression has both addition and subtraction, first collect like terms.

Example: Simplify $4xy - xw + 3xw + 3xy$

Solution: $4xy + 3xy + 3xw - xw = 7xy + 2xw$

When multiplying terms:

1. Multiply the coefficients
2. Multiply the variables (add the powers when the same variable appears)

Example: Simplify $3k \times 2k$

Solution: $3k \times 2k = (3 \times 2) \times (k \times k) = 6k^2$

Example: Simplify $4a \times 3b \times 2c$

Solution: $4a \times 3b \times 2c = (4 \times 3 \times 2) \times a \times b \times c = 24abc$

When dividing terms:

1. Divide the coefficients
2. Divide the like variables (subtract the powers)

Example: Simplify $4a \div 2a$

Solution: $4a \div 2a = \frac{4a}{2a} = \frac{4}{2} \times \frac{a}{a} = 2 \times 1 = 2$

Example: Simplify $4k^2 \div 2k$

Solution: $4k^2 \div 2k = \frac{4k^2}{2k} = \frac{4}{2} \times \frac{k^2}{k} = 2 \times k = 2k$

When simplifying algebraic expressions with multiple operations, follow the BODMAS order:

1. Brackets first
2. Orders (powers and roots)
3. Division and Multiplication (left to right)
4. Addition and Subtraction (left to right)

Example: Simplify $3a + 2 \times 5a$

Solution:

• First multiply: $2 \times 5a = 10a$
• Then add: $3a + 10a = 13a$

Example: Simplify $4 + 3 \times 2m$

Solution:

• First multiply: $3 \times 2m = 6m$
• Then add: $4 + 6m$

Example: Simplify $6n + 4n \times 2$

Solution:

• First multiply: $4n \times 2 = 8n$
• Then add: $6n + 8n = 14n$

In Tanzanian markets, algebraic simplification helps with daily buying and selling. For example, if a farmer has 6 bags of maize to sell, each bag costs $x$ shillings, and then sells an additional 4 bags at the same price, the total income is $6x + 4x = 10x$ shillings. Understanding how to simplify expressions like this helps small business owners quickly calculate earnings when trading goods at the market or when budgeting for household expenses using Tanzanian shillings.