The expression (a + b)³ appears frequently in algebra, especially when expanding binomials or solving higher-degree equations. Instead of multiplying the bracket three times, we use a ready-made identity that simplifies the process. This formula helps students save time in exams and also improves accuracy in algebraic simplifications. Whether you’re preparing for CUET, SSC, JEE, Banking, or school maths, knowing this identity makes many problems easier.
Formula for Calculating (a + b)³ Overview
| Formula | Variables | When It Is Used |
|---|---|---|
| (a + b)³ = a³ + b³ + 3a²b + 3ab² | a and b are numbers or variables | Used in algebraic expansion, simplification, and solving higher-degree equations |
What is (a + b)³ in Maths?
In mathematics, (a + b)³ represents the cube of a binomial expression. It means multiplying the expression (a + b) three times:
(a + b)(a + b)(a + b).
Instead of expanding step by step, we use the direct identity:
(a + b)³ = a³ + b³ + 3a²b + 3ab².
This identity comes from multiplying brackets in sequence:
Step 1:
(a + b)(a + b) = a² + 2ab + b²
Step 2:
(a² + 2ab + b²)(a + b)
= a³ + 3a²b + 3ab² + b³
This formula is extremely useful in algebraic expansions, polynomial simplifications, mental maths, and competitive exam questions where fast solving is required.
Examples to Calculate (a + b)³
Example 1: Expand (2 + 3)³
Step 1: Apply formula → (a + b)³ = a³ + b³ + 3a²b + 3ab²
Step 2: a = 2, b = 3
= 2³ + 3³ + 3(2²)(3) + 3(2)(3²)
= 8 + 27 + 36 + 54
Result: 125
Therefore, (2 + 3)³ = 125.
Example 2: Expand (x + 4)³
Step 1: Use formula → (a + b)³ = a³ + b³ + 3a²b + 3ab²
Step 2: a = x, b = 4
= x³ + 64 + 3(x²)(4) + 3(x)(16)
= x³ + 12x² + 48x + 64
So, (x + 4)³ = x³ + 12x² + 48x + 64.
FAQs about (a + b)³ Formula
Q1. What is the difference between (a + b)² and (a + b)³?
(a + b)² gives a square expansion, while (a + b)³ gives a cube expansion with additional terms.
Q2. Can I apply this formula for negative values?
Yes, the formula works for both positive and negative values of a and b.
Q3. In which exams is (a + b)³ commonly asked?
It appears in CUET, SSC, JEE, Banking, and all school-level algebra exams.
Q4. Is (a + b)³ equal to a³ + b³ + 3ab(a + b)?
Yes, this is another equivalent form of the identity.
Q5. Is this formula useful in real life?
Yes, it helps in solving cubic expressions, polynomial expansions, and fast mental calculations.