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Simplifying Expressions

Day 4: Combining Like Terms & The Distributive Property

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Today's Objective

To simplify algebraic expressions by combining like terms and using the distributive property.

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Part 1: Like Terms

Like terms have the exact same variables with the exact same exponents.

LIKE TERMS

$$7x \text{ and } 3x$$

NOT LIKE TERMS

$$7x \text{ and } 7y$$
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How to Combine Like Terms

Step 1: Combine Coefficients

Add or subtract the numbers in front of the variables.

Step 2: Keep the Variable

The variable part (including exponents) stays exactly the same.

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Example 1: I Do

Simplify: $${\color{#3b82f6}7x} + {\color{#ef4444}2} + {\color{#3b82f6}3x} + {\color{#ef4444}5}$$

1. Combine x-terms: $${\color{#3b82f6}7x} + {\color{#3b82f6}3x} = 10x$$

2. Combine numbers: $${\color{#ef4444}2} + {\color{#ef4444}5} = 7$$

3. Final Answer: $$10x + 7$$

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Part 2: The Distributive Property

You "distribute" the term on the outside to EVERY term on the inside of the parentheses.

Rule: $${\color{#7e22ce}a}(b + c) = {\color{#7e22ce}a}b + {\color{#7e22ce}a}c$$

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Example 2: We Do

Simplify: $${\color{#7e22ce}4}(x - 3)$$

1. Distribute to x: $${\color{#7e22ce}4} \times x = 4x$$

2. Distribute to -3: $${\color{#7e22ce}4} \times (-3) = -12$$

3. Final Answer: $$4x - 12$$

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Example 3: Putting It All Together

Simplify: $${\color{#7e22ce}2}(3x - 1) + 4x$$

1. Distribute First: $${\color{#7e22ce}2}(3x-1) = 6x-2$$

2. Combine Like Terms: $${\color{#3b82f6}6x} + {\color{#3b82f6}4x} = 10x$$

The $-2$ has no like terms, so it stays.

3. Final Answer: $$10x - 2$$

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Independent Practice

Simplify each expression.

RED (Developing)

  1. $$10y + 8 - 3y - 2$$
  2. $$3(x + 5)$$

YELLOW (Applying)

  1. $$-5(a + 2)$$
  2. $$6x + 2(x - 1)$$

GREEN (Securing)

  1. $$2(3x - 1) + 4x$$
  2. $$7y - (y - 4)$$
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Exit Ticket

Simplify the following expression:

$$3(2x + 5) - 4x$$

My simplified expression: