How to Solve Cube of Binomial?
To calculate cube of binomial, we can use the following steps:
Step 1: Identify the Binomial.
Suppose we have the binomial (a + b).
Step 2: Cube the Binomial.
Use the formula (a + b)3 = a3 + 3a2b + 3ab2 + b3 to expand the cube of the binomial.
Step 3: Apply the Binomial Cube Formula.
Substitute the values of ( a ) and ( b ) into the expanded expression.
Step 4: Simplify.
Combine like terms and simplify the expression.
Let’s consider an example for the same.
For example, if we have ( a = 2 ) and ( b = 3 ), then:
(2 + 3)3 = 23 + 3 · 22 · 3 + 3 · 2 · 32 + 33
⇒ (2 + 3)3 = 8 + 3 · 4 · 3 + 3 · 2 · 9 + 27
⇒ (2 + 3)3 = 8 + 36 + 54 + 27
⇒ (2 + 3)3 = 125
∴ (2 + 3)3 = 125
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Cube of Binomial
Cube of Binomial as the name suggests is the third power of any binomial expression. Cube of Binomial follows a specific formula, which is (a + b)3 = a3 + 3a2b + 3ab2 + b3) and (a – b)3 = a3 – 3a2b + 3ab2 – b3), where (a) and (b) are the terms of the binomial.
Table of Content
- What is Cube of Binomial?
- Meaning of Cube of Binomial
- Formula of Cube of Binomial
- Derivation of (a+b)3
- Derivation of (a-b)3
- Sum of Cubes Formula
- Derivation of Sum of Cubes Formula
- Difference of Cubes Formula
- Derivation of Difference of Cubes
- How to Solve Cube of Binomial?
- Solved Examples of Cube of Binomial
- Practice Questions of Cube of Binomial
In this article, we will learn about the sum of cubes formula, the difference of cubes formula, and how to find a cube of binomial. At the end of this article, we have provided solved numerical questions for better understanding.