Combining Like Terms

Simplifying Expressions (Combining Like Terms) 1 1 3 y− y⇒ y 2 5 10 1 3 1 3 3 ∴ y − 4 + x − y simplifies to x+ y−4 2 4 5 4 10

Example 1. Simplify 2x + 4 − 3 + x

Combine y variables:

= 2x + x + 4 − 3 (gather like variables and constants) Combine x variables: 2x + x ⇒ 3x Combine constants: 4 − 3 ⇒ 1

Example 4. Simplify −(3x − 3) + 5

∴ 2x + 4 − 3 + x simplifies to 3x + 1

= −3x + 3 + 5

(Distribute -1)

Combine constants: 3 + 5 ⇒ 8 3 Example 2. Simplify x + 4 + 5 Combine constants: 4 + ∴ x+4+

∴ −(3x − 3) + 5 simplifies to -3x + 8

3 20 3 23 ⇒ + ⇒ 5 5 5 5

3 23 simplifies to x + 5 5

Example 5. Simplify 2y − 6(y − 2) + 3 = 2y − 6y + 12 + 3

(Distribute -6)

Combine y variables: 2y − 6y ⇒ −4y 1 3 1 Example 3. Simplify y − 4 + x − y 2 4 5

Combine constants: 12 + 3 ⇒ 15

=

3 1 1 x+ y − y −4 (Gather like variables and constants) 4 2 5



Problems that Require Critical Thinking

Example 6. If a > 0, b > 0, c < 0 simplify

∴ 2y − 6(y − 2) + 3 simplifies to -4y + 15

a b c abc + + + |a| |b| |c| |abc|

a b c = 1 (since a > 0), = 1 (since b > 0), = −1 (since c < 0) |a| |b| |c| Since a > 0, b > 0, c < 0, the product of abc is less than 0 and |abc| > 0, then ∴

a b c abc + + + =1+1−1−1= 0 |a| |b| |c| |abc|

1

abc = −1. |abc|