# (x+1)^3 Formula

Before learning the (x+1)^3 expand formula, let us recall what is a binomial. A binomial is an algebraic expression with exactly two terms. We can expand (x+1)^3 by multiplying (x+1)(x+1)(x+1) manually. Let us learn the (x+1)^3 expand formula.

## What Is the (x+1)^3 Formula?

The (x+1)^{3} formula is a special algebraic identity formula used to solve cube of a special type of binomial. The (x+1)^{3} formula can be easily expanded by multiplying (x+1) thrice. To simplify the (x+1)^{3} formula further, after multiplying we just combine the like terms and the like variables together. Finally, we will arrange our algebraic expressions according to the increasing order of the exponential power.

(x+1)^{3} = x^{3} + 3x^{2} + 3x + 1

The expansion of formula (x+1)^3 is (x+1)^{3} = (x+1)(x+1)(x+1)

In our next heading we will see the further simplification of the (x+1)^{3 }formula.

## Proof of (x+1)^3 Formula

The (x+1)^{3 }formula can be verified or proved by multiplying (x + 1) three times, i.e,

(x+1)^{3} = (x+1)(x+1)(x+1)

(x+1)^{3 }= [x^{2} + x + x + 1] (x + 1)

= (x + 1) [x^{2} + 2x + 1]

= x^{3} + 2x^{2} + x + x^{2} + 2x + 1

= x^{3} + 3x^{2} + 3x + 1

Therefore, (x+1)^{3} = x^{3} + 3x^{2} + 3x + 1

## Examples on (x+1)^3 Formula

**Example 1: **Find the expansion of (a+1)^3.

**Solution:**

Using the (x+1)^3 expansion formula:

(x+1)^{3 }= x ^{3} + 3x ^{2} + x + 1

Comparing and putting the values,

(a+1)^{3 }= a^{3} + 3a^{2} + a + 1

**Answer: The expansion of (a+1)^3 is a ^{3} + 3a^{2} + a + 1.**

**Example 2:** Expand (1+t)^3.

**Solution:**

Using (x+1)^3 expansion formula:

(x+1)^{3 }= x ^{3} + 3x ^{2} + x + 1

Comparing and putting the values,

(1+t)^{3 }= t^{3} + 3t^{2} + t + 1** **

**Answer: The expansion of (1+t)^3 is t ^{3} + 3t^{2} + t + 1.**

**Example 3: **Simplify (2x +1)^{3} using (x+1)^3 expansion formula

**Solution:**

Using (x+1)^3 expansion formula:

(x+1)^{3 }= x^{3} + 3x^{2} + x + 1

Comparing and putting the values,

(2x +1)^{3 }= (2x)^{3} + 3(2x)^{2} + 2x + 1

= 8x^{3} + 12x^{2} + 2x + 1

**Answer:** (2x + 3)^{3 }= 8x^{3} + 12x^{2} + 2x + 1** **

## FAQs on (x+1)^3 Formula

### What Is the Expansion of (x + 1)^{3} Formula?

(x + 1)^{3} formula is read as x plus 1 whole cube. Its expansion is expressed as (x + 1)^{3} = x^{3} + 3x^{2} + x + 1.

### What Is the (x + 1)^{3} Formula in Algebra?

The (x + 1)^{3} formula is one of the important algebraic identities. It is read as x plus 1 whole cube. Its (x + 1)^{3} formula is expressed as (x + 1)^{3} = x^{3} + 3x^{2} + x + 1.

### How To Expand the (x + 1)^{3} Formula?

To expand (x + 1)^{3} formula we need to multiply (x + 1) three times as shown below:

- Step1: (x+1)
^{3}= (x+1)(x+1)(x+1) - Step 2: [x
^{2}+ x + x + 1] (x + 1) - Step 3: (x + 1) [x
^{2}+ 2x + 1] - Step 4: x
^{3}+ 2x^{2}+ x + x^{2}+ 2x + 1 - Step 5: x
^{3}+ 3x^{2}+ 3x + 1

### How To Use the (x + 1)^{3} Formula Give Steps?

The following steps are followed while using (x + 1)^{3} formula.

- Firstly observe the pattern of the numbers whether the numbers have whole ^3 as power or not and in the form of (x+1)^3.
- Write down the formula of (x + 1)
^{3} - (x + 1)
^{3}= x^{3}+ 3x^{2}+ x + 1. - Substitute the values in the (x + 1)
^{3}formula and simplify.

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