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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.

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

The (x+1)3 formula is a special algebraic identity formula used lớn solve cube of a specialtype 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 andthe like variables together. Finally, we will arrange our algebraic expressionsaccording 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)3formula.

Proof of(x+1)^3 Formula

The(x+1)3formula 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 + 1)=(x + 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)3=x3+3x2+ x+ 1

Comparing và putting the values,

(a+1)3= a3+3a2+ a + 1

Answer: The expansion of(a+1)^3 isa3+3a2+ a + 1.

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

Solution:

Using (x+1)^3 expansion formula:

(x+1)3=x3+3x2+ x+ 1

Comparing & putting the values,

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

Answer: The expansion of(1+t)^3is 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)3=x3+3x2+ x+ 1

Comparing và putting the values,

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

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


FAQs on (x+1)^3 Formula

What Is the Expansion of (x +1)3Formula?

(x +1)3formula 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)3Formula in Algebra?

The (x +1)3formula is one of the importantalgebraic identities. It is read as xplus 1 whole cube. Its (x +1)3formula is expressed as(x +1)3=x3+3x2+ x+ 1.

How lớn Expand the(x +1)3Formula?

To expand (x +1)3formula we need tomultiply (x + 1) three timesas shown below:

Step1: (x+1)3= (x+1)(x+1)(x+1)Step 2: (x + 1)Step 3: (x + 1)Step 4: x3 + 2x2 + x + x2 + 2x + 1Step 5: x3 + 3x2 + 3x + 1

How to lớn Use the(x +1)3Formula Give Steps?

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

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Write down the formula of(x +1)3(x +1)3=x3+3x2+ x+ 1.Substitute the values in the(x +1)3formula và simplify.