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Whole Cube Calculator

Expand and solve (a + b)³
(a + b)³ = a³ + 3a²b + 3ab² + b³
Please enter valid numbers for both a and b.

Enter values of a and b to see the expansion

Result
0
a³-
3a²b-
3ab²-
b³-
a³+3a²b+3ab²+b³-

Also verified against direct computation: (a + b)³

A Plus B Whole Cube Calculator

The A Plus B Whole Cube Calculator is a free online tool that helps you calculate the cube of the sum of two numbers using the algebraic identity (a + b)³. Enter the values of a and b to quickly calculate the result.

What is (a + b)³?

The expression (a + b)³ means that the sum of a and b is multiplied by itself three times. It can be expanded using the whole cube identity:

(a + b)³ = a³ + 3a²b + 3ab² + b³

This identity is also known as the cube of a binomial. It makes it easier to expand and calculate expressions involving the cube of the sum of two terms.

How to Use the A Plus B Whole Cube Calculator?

  1. Enter the value of a.
  2. Enter the value of b.
  3. Click the Calculate button.
  4. The calculator applies the formula (a + b)³ = a³ + 3a²b + 3ab² + b³.
  5. View the calculated result instantly.

Example of (a + b)³

Suppose a = 2 and b = 3. Using the whole cube formula:

(2 + 3)³ = 2³ + 3(2²)(3) + 3(2)(3²) + 3³
= 8 + 36 + 54 + 27
= 125

Therefore, (2 + 3)³ = 125.

Formula for the Cube of a Sum

The standard algebraic identity for the cube of the sum of two numbers is:

(a + b)³ = a³ + 3a²b + 3ab² + b³

The four terms in the expanded expression are the cube of the first term, three times the square of the first term multiplied by the second term, three times the first term multiplied by the square of the second term, and the cube of the second term.

Why Use a Whole Cube Calculator?

  • Calculate (a + b)³ quickly and accurately.
  • Understand the cube of a binomial identity.
  • Useful for algebra homework and mathematics practice.
  • Helps reduce manual calculation errors.
  • Useful for students preparing for mathematics exams.
  • Works with different positive and negative values.

Frequently Asked Questions

What is the formula for (a + b)³?

The formula for the cube of the sum of two terms is (a + b)³ = a³ + 3a²b + 3ab² + b³.

What is the meaning of (a + b)³?

It means that the sum of a and b is multiplied by itself three times: (a + b) × (a + b) × (a + b).

Can I use negative numbers in the calculator?

Yes. The formula can be applied to both positive and negative values of a and b.

What is the difference between (a + b)² and (a + b)³?

(a + b)² represents the square of the sum, while (a + b)³ represents the cube of the sum. Their algebraic identities are different.

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