Expand (x + 1)^3 using an identity

     

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 khổng lồ solve cube of a specialtype of binomial. The (x+1)3 formula can be easily expanded by multiplying (x+1) thrice. Khổng lồ simplify the (x+1)3 formula further, after multiplying we just combine the lượt thích terms andthe like variables together. Finally, we will arrange our algebraic expressionsaccording khổng lồ 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 và 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 & 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 khổng lồ 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 & simplify.