Solve Inequalities With Step
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=
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:How to lớn Use the(x +1)3Formula Give Steps?
The following steps are followed while using(x +1)3formula.
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