Ctrl+k

Simplify multi-step algebraic expressions

A multi-step algebraic expression can be interpreted as a sequence of operations and rewritten in an equivalent, simpler form using order of operations, the distributive property, and combination of like terms. This includes expressions with parentheses, variables, constants, and integer or rational coefficients; terms may be combined only when their variable parts match, supporting later equation solving and polynomial work without extending to formal factoring or advanced polynomial operations.

Detailed Explanation: Simplify multi-step algebraic expressions

To simplify a multi-step algebraic expression, follow these steps:

  1. Use the distributive property to remove parentheses.
  2. Combine like terms—terms with the same variable part.
  3. Keep unlike terms separate.

Example:

3(2x−4)+5x+73(2x-4)+5x+7

Step 1: Distribute the 33.

Multiply 33 by each term inside the parentheses:

3(2x)−3(4)+5x+73(2x)-3(4)+5x+7 6x−12+5x+76x-12+5x+7

Step 2: Group like terms.

The variable terms 6x6x and 5x5x are like terms. The constants −12-12 and 77 are also like terms:

(6x+5x)+(−12+7)(6x+5x)+(-12+7)

Step 3: Combine each group.

11x−511x-5

Therefore,

3(2x−4)+5x+7=11x−5\boxed{3(2x-4)+5x+7=11x-5}

Remember: You can combine 6x6x and 5x5x because both have the same variable part, xx. You cannot combine a variable term with a constant.

Learn by doing: Simplify multi-step algebraic expressions

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Algebraic Functions - Multiply Bracketed Terms, Same Variable (First Term)


    ?