Math Formula for (a-b-c)²
2026-02-28 11:20 Diff
https://brightchamps.com/en-us/math/math-formulas/formula-for-a-minus-b-minus-c-squared

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Last updated on September 30, 2025

In algebra, expanding expressions using formulas helps simplify calculations. One such expression is (a-b-c)², which can be expanded to simplify algebraic expressions. In this topic, we will learn the formula for (a-b-c)².

Expansion Formula for (a-b-c)²

Math Formula for Expanding (a-b-c)²

The formula for expanding (a-b-c)² is derived from the square of a trinomial. It is calculated using the formula:

(a-b-c)² = a² - 2ab - 2ac + b² + c² + 2bc

Importance of the Formula for (a-b-c)²

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Tips and Tricks to Memorize the Expansion Formula for (a-b-c)²

Students might find it tricky to remember the expansion formula for (a-b-c)². Here are some tips to help memorize it: 

  • Break down the formula into parts: (a-b-c)² = a² - 2ab - 2ac + b² + c² + 2bc 
  • Practice expanding similar expressions to reinforce memory 
  • Use mnemonics like "square each term, double the products, and add them up"

Real-Life Applications of Expanding (a-b-c)²

Expanding expressions like (a-b-c)² has practical applications in various fields. Here are some examples: 

  • In physics, to calculate the change in energy or force in systems 
  • In engineering, to model and solve structural problems 
  • In computer science, to optimize algorithms involving polynomial calculations

Common Mistakes and How to Avoid Them While Using (a-b-c)² Formula

Students often make errors when expanding (a-b-c)². Here are some common mistakes and ways to avoid them:

Problem 1

Expand the expression (x-2-y)².

Okay, lets begin

x² - 2x(2) - 2xy + (2)² + y² + 2(2)y

Explanation

First, apply the formula (a-b-c)²: = x² - 2(x)(2) - 2(x)(y) + (2)² + y² + 2(2)(y) = x² - 4x - 2xy + 4 + y² + 4y

Well explained 👍

Problem 2

Expand the expression (3-a-b)².

Okay, lets begin

9 - 2(3)(a) - 2(3)(b) + a² + b² + 2(a)(b)

Explanation

First, apply the formula (a-b-c)²: = (3)² - 2(3)(a) - 2(3)(b) + a² + b² + 2(a)(b) = 9 - 6a - 6b + a² + b² + 2ab

Well explained 👍

Problem 3

Expand the expression (5-m-n)².

Okay, lets begin

25 - 10m - 10n + m² + n² + 2mn

Explanation

First, apply the formula (a-b-c)²: = (5)² - 2(5)(m) - 2(5)(n) + m² + n² + 2(m)(n) = 25 - 10m - 10n + m² + n² + 2mn

Well explained 👍

FAQs on (a-b-c)² Formula

1.What is the formula for expanding (a-b-c)²?

The formula to expand (a-b-c)² is: (a-b-c)² = a² - 2ab - 2ac + b² + c² + 2bc

2.Why is the (a-b-c)² formula important?

The formula helps simplify algebraic expressions, solve quadratic equations, and perform polynomial operations.

3.How can I avoid mistakes when using (a-b-c)² formula?

To avoid mistakes, ensure each term is squared, the correct signs are used, products are doubled, and expand without skipping steps.

4.What are some real-life applications of expanding (a-b-c)²?

This formula is used in physics for energy calculations, engineering for structural modeling, and computer science for algorithm optimization.

Glossary for (a-b-c)² Formula

  • Square of a trinomial: A mathematical expression involving the square of three terms, expanded using specific formulas. 
  • Expansion: The process of expressing a mathematical entity as a sum or an extended form. 
  • Algebraic identity: An equation true for all values of its variables, used to simplify expressions. 
  • Polynomial: An expression consisting of variables and coefficients, involving operations of addition, subtraction, and multiplication. 
  • Quadratic equation: A polynomial equation of the second degree, often solved using various algebraic methods.

Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.