Simplify Algebraic Expression Calculator

Enter Calculation

Simplify a linear expression of the form a(x) + b combined into one line. Enter the coefficients of each term to combine like terms.

First x-coefficient

Second x-coefficient

First constant

Second constant

Distribution multiplier (applies to the whole sum, e.g. 2 for 2(...))

Results

Simplified Expression

5x + 9

like terms combined and distribution applied

x-coefficient	5
Constant term	9

What this calculator does

The Simplify Algebraic Expression Calculator reduces a linear expression to its simplest standard form, \(ax + b\). It works by combining like terms — grouping all the x-terms and all the constant terms — and then applying any distribution multiplier that scales the whole sum. This is the everyday algebra skill used in equation solving, factoring, and simplifying before graphing a line.

Like terms are grouped and combined to reduce the expression to \(ax + b\) form.

How to use it

Enter the two x-coefficients (the numbers in front of x) and the two constants you want to combine. If your expression is wrapped in a multiplier such as 2(...), enter that as the distribution multiplier; otherwise leave it as 1. The calculator adds the like terms and multiplies the result by the distribution factor, returning a clean \(ax + b\) expression.

The formula explained

Starting from \(a_1x + b_1 + a_2x + b_2\), like terms are combined to give \((a_1 + a_2)x + (b_1 + b_2)\). Multiplying by the distribution factor \(k\) gives the following:

$$\text{Result} = \text{Mult}\Big[\left(\text{Coef}_1 + \text{Coef}_2\right)x + \left(\text{Const}_1 + \text{Const}_2\right)\Big]$$

The x-coefficient and the constant are reported separately so you can read off the slope and intercept of the resulting line.

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Distribution spreads the outside factor \(k\) across each term inside the brackets.

Worked example

Suppose you want to simplify \(2[(3x + 5) + (2x + 4)]\). The x-coefficients are 3 and 2, summing to 5; the constants are 5 and 4, summing to 9. With distribution factor 2, the x-coefficient becomes

$$5 \times 2 = 10$$

and the constant becomes

$$9 \times 2 = 18$$

The simplified expression is \(10x + 18\).

FAQ

What if there is no multiplier? Set the distribution multiplier to 1; the expression is then just the combined like terms.

Can I use negative numbers? Yes. Enter negative coefficients or constants directly and they will be added with their signs.

Does it handle non-linear terms? No, this tool focuses on linear expressions in a single variable x reduced to \(ax + b\) form.