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102 LearnersLast updated on August 9, 2025
Math Formula for (a + b)²
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 (a + b)² formula is a crucial algebraic identity.
Let's learn how to expand the expression (a + b)² using this 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
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
The (a + b)² formula is widely used in algebra and geometry. Here are some reasons why it's important: It simplifies the process of expanding binomials.
It's used in solving quadratic equations and in finding perfect squares. It helps in understanding the properties of algebraic expressions.
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.
Mistake 1
Forgetting the Middle Term
Students often forget to include the middle term 2ab when expanding (a + b)². To avoid this, always remember the formula: (a + b)² = a² + 2ab + b².
Mistake 2
Incorrectly Squaring Individual Terms
A common mistake is to square a and b separately, leading to a² + b². Always apply the formula to get a² + 2ab + b².
Mistake 3
Confusing (a + b)² with a² + b²
Students sometimes confuse (a + b)² with a² + b². Remember that (a + b)² includes the additional 2ab term.
Mistake 4
Errors in Calculation
Calculation errors occur when students multiply terms incorrectly. Double-check each multiplication step to ensure accuracy.
Mistake 5
Misinterpreting the Formula
Some students misinterpret the formula as (a² + b²) instead of (a + b)². Always expand using the correct formula to avoid errors.
Examples of Problems Using the (a + b)² Formula
Problem 1
Expand (3 + 4)² using the formula.
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
Problem 2
Expand (x + 5)² using the formula.
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
Problem 3
Expand (2a + 3b)² using the formula.
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
Problem 4
Expand (m + n)² using the formula.
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
Problem 5
Expand (5x + 2)² using the formula.
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
FAQs on the (a + b)² Formula
1.What is the formula for (a + b)²?
2.How do you derive the (a + b)² formula?
3.What is the result of expanding (4 + 3)²?
4.How can I remember the (a + b)² formula?
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.
- Quadratic: A polynomial of degree two.
- 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.
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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.
