Algebraic expressions contain numbers, variables, and operators and can be simplified using the distributive property and by combining like terms. The document provides examples of algebraic expressions that can be simplified by first distributing all terms inside parentheses and then combining like terms, such as 3(4n + 2) + n, which is simplified to 12n + 6 + n = 13n + 6.

2. Algebraic Expression –
a mathematical phrase that can
contain numbers, variables (like x or y)
and operators (like +, -, x, ÷ ).
Like Terms –
terms that have the same variables
and powers. (The coefficients do not
need to match.)

3. Distributive Property –
When we use the distributive
property, we are multiplying each
term inside the parentheses with the
term outside of the parentheses.

4. First, distribute to get rid of all
parentheses.
Then, combine like terms.

5. Simplify each expression.
3(4n + 2) + n
7x – (2x – 3) + 1

6. Simplify each expression.
5(3x + 1) – 4x
4r – 6(1 + r)

7. -2(m + 5) + 6m – 1
4(x + 7) – 2(1 + 5x)

8. -5(2 – b) + 3b – 7
2(3k + 6) – 4(1 – 2k)