Goal: Find the Pieces of an Expression

Tiny Concept

A term is a single piece of an expression.

Terms are separated by:

• plus signs (+)
• minus signs (−)

Think:

Terms are the chunks between the + and − signs.

Recipe Box

How to Find Terms

Step 1:

Look for + and − signs.

Step 2:

Split the expression into chunks.

Step 3:

Everything between the signs is a term.

See One

Find the terms.

3x+4x−7+2

The plus and minus signs split the expression into pieces.

Terms:

3x

4x

−7

2

There are 4 terms.

Try One

Find the terms.

5y+9−2y+4

Terms:

Do One

Find the terms.

1

8x+3

2

7a−5+2a

3

4m+6−3m+8

Mixed Check

1

How many terms are in

6x+4−2x+9

A) 2

B) 3

C) 4

D) 5

2

Which is a term in

9y−4+2

A) 9

B) y

C) 9y

D) -4+2

3

How many terms are in

7a+2b−8

A) 2

B) 3

C) 4

D) 5

Tiny Reminder

Plus and minus signs separate terms.

Goal: Know Which Terms Can Combine

Tiny Concept

Not all terms can combine.

Terms can combine only if the variable part matches exactly.

Recipe Box

Like Terms Recipe

Step 1:

Circle the terms.

Step 2:

Find matching variable parts.

Step 3:

Combine coefficients.

Important Idea

The variable part must match exactly.

See One

Simplify:

3x+4x−7+2

Find like terms.

3x + 4x = 7x

AND

−7+2=−5

Answer:

7x−5

Try One

Simplify:

5y+2y+4

Combine:

5y + ____ =____y

Do One

1

8x+3x

2

4a+7a−2

3

9m−3m+6

Mixed Check

1

Simplify:

6x+2x

A) 8x

B) 12x

C) 8x2

D)12

2

Which pair are like terms?

A) 3x, 4x

B) 3x, 4y

C) $x^2 , x$

D) 2a, 2b

3

Simplify:

7y+3y−5

A) 10y−5

B) 21y−5

C) 10y

D) 21y

Term → Like Term → Expression

A term is a piece.

3x

An expression is a collection of terms.

3x+4x−7 + 2

Like terms are pieces that belong together.

3x and 4x can combine to make 7x

Unit 7: Expressions, Distribution, Combining Like Terms, & Factoring

Why This Matters

By itself, distribution feels simple:

3(x+4)

But on the SAT, distribution is rarely the final goal.

Instead, it is usually one step inside a larger problem involving:

• functions
• equations
• graphing
• quadratics
• systems
• data analysis
• modeling

The challenge is often recognizing:

"Oh, I need to distribute here."

before you can continue solving.

SAT Application #1

Expression Simplification

The SAT often asks:

Which expression is equivalent to...

Example:

4(x+3)−2(x−1)

Students must: Distribute.

4x+12−2x+2

Combine like terms.

2x+14

This is one of the most common SAT algebra patterns.

Difficulty:

⭐ Easy-Medium

SAT Application #2

Function Evaluation

The SAT loves functions.

Example:

If f(x)=3(x+4)−5 what is the value of f(2)?

Many students immediately substitute.

Strong students recognize they may need to simplify first.

f(x)=3x+12−5

Combine like terms and substitute.

f(x)=3x+7

Then:

f(2)=13

Difficulty:

⭐⭐ Medium

SAT Application #3

Graphing Linear Functions

Example: A student is given y=2(x+3)−1

The SAT asks:

What is the y-intercept?

You cannot easily identify the y-intercept until you distribute.

y=2x+6−1

Simplify:

y=2x+5

Now the y-intercept is obvious. (y-int is 5).

Notice:

The question is about graphing.

The hidden skill is distribution.

Difficulty:

⭐⭐ Medium

SAT Application #4

Solving Equations

Example:

5(x+2)=3x+18

Distribute.

5x+10=3x+18

Move variables together. (5x and 3x & 10 and 18)

2x=8

x=4

Students often think:

"This is an equation problem."

But the first skill tested is actually distribution.

Difficulty:

⭐⭐ Medium

SAT Application #5

Quadratics

Example:

(x+3)(x+5)

The SAT may ask:

Which expression is equivalent?

Students must distribute twice.

$x^2+5x+3x+15$

$x^2+8x+15$

Notice:

This is a quadratic question.

But it depends on the distributive property.

Difficulty:

⭐⭐⭐ Hard

SAT Application #6

Factoring Quadratics

Example:

$x^2+8x+15$

The SAT asks:

Which expression is equivalent?

Students must factor.

(x+3)(x+5)

Factoring is just distributive property backwards.

This is why learning factoring now matters later.

Difficulty:

⭐⭐⭐ Hard

SAT Application #7

Zeros of Functions

Example:

The function y=$x^2+8x+15$ has x-intercepts at which values?

Strong students factor.

(x+3)(x+5)=0

Then solve.

x=−3

x=−5

The SAT question looks like graphing.

The hidden skill is factoring.

Difficulty:

⭐⭐⭐ Hard

SAT Application #8

Geometry Formulas

Example:

The perimeter of a rectangle is

P=2(L+W)

The SAT asks:

Which expression is equivalent?

Students distribute.

P=2L+2W

The question appears to be geometry.

The skill being tested is algebraic manipulation.

Difficulty:

⭐⭐ Medium

SAT Application #9

Data & Modeling

Example:

A company charges 8(x+5) dollars for a service.

The SAT asks:

Which expression represents the total cost?

Students distribute.

8x+40

Again:

Real-world context.

Middle-school skill.

Difficulty:

⭐⭐ Medium

What SAT Students Should Notice

Many SAT questions disguise algebra skills inside other topics.

Big Idea

The SAT rarely tests distribution as the destination.

It tests distribution as the bridge.

Students who can immediately recognize:

"I need to distribute."

or

"I should factor this."

save enormous amounts of time because they can see the structure underneath the question instead of getting distracted by the topic wrapped around it.