Question

combining like terms
like terms: elements of an expression that _______
constants
only match other _______
examples: non - examples:
variables
only match when they have the same _____ and _____
examples: non - examples:
combining like terms:
_______ terms can be combined (or simplified) by adding or subtracting
terms must have the same _____ & same _____ to be combined!
the _____ property allows us to rewrite the expression in a different _____ without changing the overall value!
examples:

1. 3a + 4a
2. 7y - 3y + 2
3. 3x - 4 + x
4. 5 - 3s - 8 + 6s
5. 4x² - 3x + x² + 5x

Explanation:

Step1: Define like terms

Like Terms: Elements of an expression that share identical variable parts (or are constants)

Step2: Fill constants section

Only match other constants

• Examples: $5$, $-2$, $10$
• Non-Examples: $3x$, $7y^2$, $a$

Step3: Fill variables section

Only match when they have the same variable and exponent

• Examples: $4x$ & $7x$, $2y^2$ & $9y^2$
• Non-Examples: $3x$ & $3y$, $5x$ & $5x^2$

Step4: Fill combining like terms rules

Like terms can be combined (or simplified) by adding or subtracting
Terms must have the same variable & same exponent to be combined!
The commutative property allows us to rewrite the expression in a different order without changing the overall value!

Step5: Simplify example 1

Combine coefficients of $a$
$3a + 4a = (3+4)a = 7a$

Step6: Simplify example 2

Combine coefficients of $y$
$7y - 3y + 2 = (7-3)y + 2 = 4y + 2$

Step7: Simplify example 3

Combine coefficients of $x$
$3x - 4 + x = (3+1)x - 4 = 4x - 4$

Step8: Simplify example 4

Combine constants and $s$ terms
$5 - 3s - 8 + 6s = (5-8) + (-3+6)s = -3 + 3s$

Step9: Simplify example 5

Combine $x^2$ terms and $x$ terms
$4x^2 - 3x + x^2 + 5x = (4+1)x^2 + (-3+5)x = 5x^2 + 2x$

Answer:

Like Terms & Classification:

Like Terms: Elements of an expression that share identical variable parts (or are constants)

Constants

Only match other constants

Examples	Non-Examples

Variables

Only match when they have the same variable and exponent

Examples	Non-Examples

Combining Like Terms Rules:

• Like terms can be combined (or simplified) by adding or subtracting
• Terms must have the same variable & same exponent to be combined!
• The commutative property allows us to rewrite the expression in a different order without changing the overall value!

Simplified Examples:

1. $7a$
2. $4y + 2$
3. $4x - 4$
4. $3s - 3$
5. $5x^2 + 2x$