Expand x 3 3

Expand x 3 3 DEFAULT

(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.

x plus 1 whole cube 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 = x3 + 3x2 + 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)formula.

Proof of (x+1)^3 Formula

The (x+1)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)= [x2 + x + x + 1] (x + 1)
= (x + 1) [x2 + 2x + 1]
= x3 + 2x2 + x + x2 + 2x + 1
= x3 + 3x2 + 3x + 1

Therefore, (x+1)3 = x3 + 3x2 + 3x + 1

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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)= x 3  + 3x 2 + x  + 1

Comparing and putting the values,

(a+1)= a3  + 3a2 + a  + 1

Answer: The expansion of (a+1)^3 is  a3  + 3a2 + a  + 1.

Example 2: Expand (1+t)^3.

Solution:     

Using (x+1)^3 expansion formula:

(x+1)= x 3  + 3x 2 + x  + 1

Comparing and putting the values,

(1+t)= t3  + 3t2 + t  + 1                                                                  

Answer: The expansion of (1+t)^3 is t3  + 3t2 + t  + 1.

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

Solution:

Using (x+1)^3 expansion formula:

(x+1)= x3 + 3x2 + x  + 1

Comparing and putting the values,

(2x +1)= (2x)3 + 3(2x)2 + 2x  + 1
= 8x3 + 12x2 + 2x + 1

Answer: (2x + 3)= 8x3 + 12x2 + 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 = x3 + 3x2 + 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 = x3 + 3x2 + 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: [x2 + x + x + 1] (x + 1)
  • Step 3: (x + 1) [x2 + 2x + 1]
  • Step 4:  x3 + 2x2 + x + x2 + 2x + 1
  • Step 5: x3 + 3x2 + 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 = x3 + 3x2 + x  + 1.
  • Substitute the values in the (x + 1)3 formula and simplify.
Sours: https://www.cuemath.com/x-plus-1-cube-expand-formula/

expand calculator

Summary :

Calculator is able to expand an algebraic expression online.

expand online

Description :

In mathematics, to expand an expression or to expand a product that is transformed into algebraic sum. This calculator allows to expand all forms of algebraic expressions online, it also helps to calculate special expansions online (the difference of squares, the identitiy for the square of a sum and the identity for the square of a difference). For simple expansions, the calculator gives the calculation steps.

Expand algebraic expressions

the function allows to expand online all forms of mathematical expressions, the expression can be alphanumeric, ie it can contain numbers and letters :

  • Expand the following product (3 x+ 1) (2 x+ 4) `(3x+1)(2x+4)` returns `3*x*2*x+3*x*4+2*x+4`
  • Expand this algebraic expression `(x+2)^3` returns `2^3+3*x*2^2+3*2*x^2+x^3`
Note that the result is not returned as the simplest expression in order to be able to follow the steps of calculations. To simplify the results, simply use the reduce function.

Special expansions online

The function expand makes it possible to expand a product, it applies to all mathematical expressions, especially the following identities :

  • the identitiy for the square of a sum : It allows to expand online expressions of the form `(a+b)^2`
  • the identity for the square of a difference : It allows to expand online expressions of the form `(a-b)^2`
  • the difference of squares : It allows to expand online expressions of the form `(a-b)(a+b)`

Use of Newton's binomial formula

Newton's binomial formula is written : `(a+b)^n=sum_(k=0)^{n} ((n),(k)) a^k*b^(n-k)`. The numbers `((n),(k))` are the binomial coefficients, they are calculated using the following formula : `((n),(k))=(n!)/(k!(n-k)!)`.

We note, that by replacing n by 2, we can find remarkable identities.

The calculator uses Newton's formula to develop expressions of the form `(a+b)^n`.

Expand and simplify an expression

The calculator allows you to expand and collapse an expression online, to achieve this, the calculator combines the functions collapse and expand. For example it is possible to expand and reduce the expression following `(3x+1)(2x+4)`, The calculator will returns the expression in two forms :

  • expanded expression `3*x*2*x+3*x*4+2*x+4`
  • expanded and reduced expression `4+14*x+6*x^2`.

Calculator is able to expand an algebraic expression online.

Syntax :

expand(expression), expression is expression algebraic to expand.

Examples :

Here somes examples of using the computer to expand algebraic expression: Calculate online with expand (expand calculator)
Sours: https://www.solumaths.com/en/math-apps/calc-online/expand
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Most Used Actions

\mathrm{simplify} \mathrm{solve\:for} \mathrm{expand} \mathrm{factor} \mathrm{rationalize}
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