Quick answer

Like terms have the same variable and exponent. Add or subtract their coefficients only; the exponent stays fixed.

Formula

  • 3x² + 5x² → 8x²
  • 4x − x → 3x

Introduction

Combining like terms is the simplification step inside every polynomial add/subtract problem. Practice here, then verify in the Adding and Subtracting Polynomials Calculator.

Students sometimes combine unlike terms (x and x²) or add exponents; this guide focuses on correct coefficient work only.

Definition of like terms

x² and 7x² are like terms; x and x² are not. Constants are like terms with each other because they share exponent 0.

Official add/subtract rules live in adding and subtracting polynomials rules; like-term merging is how you execute those rules term by term.

Coefficients may be integers, fractions, or decimals; the like-term test still depends only on the exponent on x.

Coefficient operations

  • Addition of like terms: (a + b)x^k when both terms are x^k.
  • Subtraction: (a − b)x^k.
  • Include 0 for missing powers when aligning full polynomials.

When simplifying a single expression, scan for matching exponents anywhere in the sum. When adding two polynomials, like terms may appear once in P and once in Q.

After combining, polish the answer using simplifying polynomial expressions checklist: standard form and no stray zero terms.

Step-by-step guide

  1. Circle or highlight matching powers. Group all x³ terms, then all x², and so on down to constants. Unlike terms stay separate.
  2. Combine coefficients within each group. Use addition or subtraction rules for integers. Show intermediate sums when learning.
  3. Write standard form. List terms from highest degree to constant. Drop groups whose coefficient became 0.
  4. Cross-check with the tool. Enter simplified P and Q in polynomial calculator; R(x) should already reflect merged like terms.

Example: simplifying before adding

Inside one polynomial: 5x³ − 2x³ + x = (5 − 2)x³ + x = 3x³ + x.

Across two polynomials: (2x² + x) + (3x² − x) merges x² to 5x² and x to 0x, giving 5x².

Enter equivalent inputs in the polynomial calculator to see the same merged result.