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If you have 3 boxes of pizza plus 5incash,andafriendbrings2boxesofpizzaplus5 in cash, and a friend brings 2 boxes of pizza plus 10 in cash, you instinctively combine the boxes with boxes and the cash with cash.
In algebra, we use that exact same sorting rule whenever we combine expressions made of variables and numbers.

Like Terms and Linear Expressions

A linear expression is a math phrase where every variable has an exponent of 1, such as 3x+53x + 5 or 2x−4y+72x - 4y + 7.
We can only combine like terms, which are terms sharing the exact same variable part, by adding or subtracting their coefficient (the number multiplying the variable).
How do we neatly combine two multi-term groups into one simplified expression?

Adding Expressions Horizontally

To add expressions horizontally, drop the grouping parentheses and rearrange like terms so they sit next to each other.
Let's add (4x+7)+(2x−3)(4x + 7) + (2x - 3). Regrouping gives (4x+2x)+(7−3)(4x + 2x) + (7 - 3), which simplifies directly to 6x+46x + 4.
Horizontal grouping works well for short expressions, but what if you have trinomials with multiple variables?

Adding Expressions Vertically