On this page you will read the information of a+b Whole Cube.

## a+b Whole Cube

The (a + b)^{3} formula is used to find the cube of a binomial. This formula is also used to factorize some special types of trinomials. This formula is :

- one of the algebraic identities.
- the formula for the cube of the sum of two terms.

Let us understand (a + b)^{3 }formula in detail in the following section.

## What Is the (a + b)^{3} Formula?

To find the cube of a binomial, we will just multiply (a + b)(a + b)(a + b). (a + b)^{3} formula is also an identity. It holds true for every value of a and b.The (a + b)^{3} is given as,

(a + b)^{3} = (a + b)(a + b)(a + b)

= (a^{2} + 2ab + b^{2})(a + b)

= a^{3} + a^{2}b + 2a^{2}b + 2ab^{2} + ab^{2} + b^{3}

= a^{3} + 3a^{2}b + 3ab^{2} + b^{3}

= a^{3} + 3ab(a+b) + b^{3}

Therefore, (a + b)^{3} formula is :

**(a + b) ^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}**

## Examples on (a + b)^{3} Formula

**Example 1**. Solve the following expression using suitable algebraic identity: (2x + 3y)^{3}

**Solution :**

To find : (2x + 3y)^{3}

Using (a + b)^{3} Formula,

(a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}

= (2x)^{3} + 3 × (2x)^{2} × 3y + 3 × (2x) × (3y)^{2} + (3y)^{3}

= 8x^{3} + 36x^{2}y + 54xy^{2} + 27y^{3}

**Answer : (2x + 3y) ^{3} = 8x^{3} + 36x^{2}y + 54xy^{2} + 27y^{3}**

**Example 2**. Find the value of x^{3} + 8y^{3} if x + 2y = 6 and xy = 2.

**Solution :**

To find: x^{3} + 8y^{3}

Given: x + 2y = 6

xy = 2

Using (a + b)^{3} formula,

(a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}

Here, a = x; b = 2y

Therefore,

(x + 2y)^{3} = x^{3} + 3 × x^{2} × (2y)^{ }+ 3 × x × (2y)^{2} + (2y)^{3}

(x + 2y)^{3} = x^{3} + 6x^{2}y + 12xy^{2} + 8y^{3}

6^{3}** ^{ }**=

**x**

^{3}+ 6xy(x + 2y) + 8y

^{3}

216 = x

^{3}+ 6 × 2 × 6 + 8y

^{3}

x

^{3}+ 8y

^{3}= 144

**Answer: x ^{3} + 8y^{3} = 144**

**Example 3**. Solve the following expression using (a + b)^{3} formula : (5x + 2y)^{3}

**Solution :**

To find: (5x + 2y)^{3}

Using (a + b)^{3} Formula,

(a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}

= (5x)^{3} + 3 × (5x)^{2} × 2y + 3 × (5x) × (2y)^{2} + (2y)^{3}

= 125x^{3} + 150x^{2}y + 60xy^{2} + 8y^{3}

**Answer: (5x + 2y) ^{3} = 125x^{3} + 150x^{2}y + 60xy^{2} + 8y^{3}**

### FAQ

**Q.1 What is the A+ B whole cube?**

**Ans.** (a + b) whole cube formula says: (a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3.} To find the cube of a binomial, we will just multiply (a + b)(a + b)(a + b). (a + b)^{3} formula is also an identity. It holds true for every value of a and b.

**Q.2 What is the formula for a**

**+ b**^{3}**?**^{3}**Ans.** A polynomial equation, commonly called an algebraic expression, is a mathematical formula of the type : P=0. Formulas for a3+b3 are : **a^{3} + b^{3} = (a + b) (a² – ab + b²)**

**Q.3 What is cube formula?**

**Ans.** Length = Breadth = Height = a. Thus, the measure of each edge of the cube = a. Therefore, the volume of cube formula is **a × a × a = a ^{3}**.

**Q.4 What is alpha minus beta?**

**Ans.** α – β = **√(α + β)² – 4αβ**

**Q.5 How do you write a B 3 formula?**

**Ans.** (a + b)^{3} formula is also an identity. It holds true for every value of a and b. Therefore, (a + b)^{3} **Formula is :** **(a + b) ^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}**.

**Q.6 What is 1 cube in maths?**

**Ans.** The value of cube 1 to 30 is the list of numbers obtained by multiplying the same integer three times. **For Example,** 1^{3} = 1×1×1 = 1, 2^{3} = 2×2×2 = 8, 3^{3} = 3×3×3 = 27, 4^{3} = 4×4×4 = 64, and so on.

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