Math Formula for (a + b)²
2026-02-28 23:13 Diff
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Last updated on August 9, 2025

In algebra, the formula for the square of a binomial is essential for expanding expressions. The formula for (a + b)² is used to calculate the square of the sum of two terms. In this topic, we will learn the formula for (a + b)² and its applications.

Understanding the (a + b)² Formula

The Math Formula for (a + b)²

The formula for (a + b)² is given by: (a + b)² = a² + 2ab + b²

This formula is derived by multiplying the binomial (a + b) by itself.

Derivation of the (a + b)² Formula

To derive the formula for (a + b)², we multiply the binomial by itself:

(a + b) × (a + b) = a(a + b) + b(a + b) = a² + ab + ab + b² = a² + 2ab + b²

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Examples Using the (a + b)² Formula

Let's explore some examples to understand how to apply the (a + b)² formula.

Example 1: Expand (3 + 4)² using the formula.

Example 2: Expand (x + 5)² using the formula.

Importance of the (a + b)² Formula

Tips and Tricks for Memorizing the (a + b)² Formula

Students often find memorizing formulas challenging. Here are some tips to master the (a + b)² formula: Visualize the formula as (a + b)(a + b) to remember the steps.

Use the mnemonic "square the first, twice the product, square the last" to recall: a², 2ab, b².

Practice expanding different binomials to reinforce the formula.

Common Mistakes and How to Avoid Them While Using the (a + b)² Formula

Students make errors when applying the (a + b)² formula. Here are some common mistakes and how to avoid them.

Problem 1

Expand (3 + 4)² using the formula.

Okay, lets begin

The expansion is 49.

Explanation

Using (a + b)² = a² + 2ab + b²,

where a = 3 and b = 4: (3 + 4)² = 3² + 2(3)(4) + 4² = 9 + 24 + 16 = 49

Well explained 👍

Problem 2

Expand (x + 5)² using the formula.

Okay, lets begin

The expansion is x² + 10x + 25.

Explanation

Using (a + b)² = a² + 2ab + b²,

where a = x and b = 5:

(x + 5)² = x² + 2(x)(5) + 5² = x² + 10x + 25

Well explained 👍

Problem 3

Expand (2a + 3b)² using the formula.

Okay, lets begin

The expansion is 4a² + 12ab + 9b².

Explanation

Using (a + b)² = a² + 2ab + b²,

where a = 2a and b = 3b

(2a + 3b)² = (2a)² + 2(2a)(3b) + (3b)² = 4a² + 12ab + 9b²

Well explained 👍

Problem 4

Expand (m + n)² using the formula.

Okay, lets begin

The expansion is m² + 2mn + n².

Explanation

Using (a + b)² = a² + 2ab + b²,

where a = m and b = n

(m + n)² = m² + 2(m)(n) + n² = m² + 2mn + n²

Well explained 👍

Problem 5

Expand (5x + 2)² using the formula.

Okay, lets begin

The expansion is 25x² + 20x + 4.

Explanation

Using (a + b)² = a² + 2ab + b²,

where a = 5x and b = 2

(5x + 2)² = (5x)² + 2(5x)(2) + 2² = 25x² + 20x + 4

Well explained 👍

FAQs on the (a + b)² Formula

1.What is the formula for (a + b)²?

The formula for (a + b)² is: (a + b)² = a² + 2ab + b²

2.How do you derive the (a + b)² formula?

The (a + b)² formula is derived by multiplying the binomial by itself: (a + b)(a + b) = a² + 2ab + b²

3.What is the result of expanding (4 + 3)²?

The result of expanding (4 + 3)² is 49.

4.How can I remember the (a + b)² formula?

You can remember the formula by using the mnemonic: "square the first, twice the product, square the last" for a², 2ab, b².

5.What is the expanded form of (x + 7)²?

Glossary for the (a + b)² Formula

  • Binomial: An algebraic expression containing two terms.
  • Expansion: The process of multiplying out the terms of an expression.
  • Algebra: A branch of mathematics dealing with symbols and the rules for manipulating those symbols.
  • Perfect square: An expression that is the square of a binomial.

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.