Day 4 Presentation

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Unit 1: Algebraic Expressions

Day 4: Simplifying Expressions

Today's Objective

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

Part 1: Like Terms

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

LIKE TERMS

$$7x$$and$$3x$$

NOT LIKE TERMS

$$7x$$and$$7y$$

Combining Like Terms

1. Add or subtract the numbers in front (the coefficients).
2. Keep the variable part exactly the same.

I Do: Let's Simplify

Problem:

$$7x$$ $$+$$ $$2$$ $$+$$ $$3x$$ $$+$$ $$5$$

1. Identify Like Terms

2. Combine x-terms:

$$7x$$ $$+$$ $$3x$$ $$=$$ $$10x$$

3. Combine numbers:

$$2$$ $$+$$ $$5$$ $$=$$ $$7$$

Final Answer:

$$10x + 7$$

Part 2: The Distributive Property

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

Rule:

$$a$$ $$(b + c)$$ $$=$$ $$a$$$$b$$ $$+$$ $$a$$$$c$$

We Do: Distribute Together

Problem:

$$4$$ $$(x - 3)$$

1. Distribute to the first term:

$$4$$$$\times$$$$x$$$$=$$$$4x$$

2. Distribute to the second term:

$$4$$$$\times$$$$(-3)$$$$=$$$$-12$$

Final Answer:

$$4x - 12$$

Putting It All Together

Problem:

$$2$$ $$(3x - 1)$$ $$+$$ $$4x$$

1. Distribute First:

$$2$$ $$(3x-1)$$ $$=$$ $$6x-2$$

Now the problem is:

$$6x$$ $$-$$ $$2$$ $$+$$ $$4x$$

2. Combine Like Terms:

$$6x$$ $$+$$ $$4x$$ $$=$$ $$10x$$

The $$-2$$ has no like terms.

Final Answer:

$$10x - 2$$

Independent Practice

RED

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

YELLOW

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

GREEN

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

Exit Ticket

Simplify the following expression:

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