Simplifying Expressions

Simplifying makes expressions easier to work with by combining like terms.

What Are Like Terms?

Like terms have the same variable raised to the same power.

Like Terms	Not Like Terms
$3x$ and $5x$	$3x$ and $3y$
$2x^2$ and $-x^2$	$x^2$ and $x$
$7$ and $-3$	$4$ and $4x$

Combining Like Terms

Add or subtract the coefficients, keep the variable the same.

Example 1

$3x + 5x = 8x$

Example 2

$7y - 2y = 5y$

Example 3

$4x + 3 + 2x - 1$

Group like terms: $(4x + 2x) + (3 - 1) = 6x + 2$

The Distributive Property

When you have parentheses, distribute (multiply) first:

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

Example 4

$3(x + 4) = 3x + 12$

Example 5

$2(3x - 5) = 6x - 10$

Example 6

$-(x + 2) = -x - 2$

(Distributing $-1$)

Putting It Together

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

1. Distribute: $2x + 6 + 4x - 5$
2. Group like terms: $(2x + 4x) + (6 - 5)$
3. Combine: $6x + 1$