The a3+b3formula is called the sumof cubes (of two numbers) formula. The a cube plus b cube formulais used lớn find the sum of the two cubes without actually calculating the cubes. Also, it is used khổng lồ factorize the binomials of cubes.In this section, we will be discussing the various aspects of the a3+b3formula, along with solved examples, and understvà where the identity can be involved.

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What Is a^3+b^3 Formula?

Thea3+b3formula can beverified, bymultiplying(a + b) (a2-ab + b2) and see whether you get a3+ b3.The a3+ b3formula or the difference ofcubesformula is explained below:

a3+b3Formula = a3+ b3= (a +b) (a2- ab + b2)

You can rethành viên these signs using the following trichồng.


Let us learn thea3+b3formula with a few solved examples.

Proof of a^3+ b^3Formula

Let us see the verification of a cube plus b cube formula here. To prove or verify thata3+ b3= (a +b) (a2- ab + b2) we need to prove here LHS = RHS. Lets begin with the following steps.LHS =a3+ b3On Solving RHS side we get,= (a +b) (a2- ab + b2)On multiplying the a và b separatelywith(a2-ab + b2) we get= a (a2- ab + b2) + b(a2- ab + b2)= a3 - a2b + ab2 + a2b - ab2+ b3= a3 - a2b + a2b + ab2- ab2+ b3=a3- 0 + 0 + b3=a3+ b3Hence proved, LHS = RHS

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Examples on a^3+b^3Formula

Example 1:Find the value of 1023+ 83by using the a^3+b^3 formula.

Solution:To find:1023+ 83.Let us assume that a = 102 and b = 8.We will substitute these in the formula ofa3+ b3i.e.,a3+ b3= (a + b) (a2- ab + b2)1023+83= (102+8)(1022- (102)(8)+82)= (110) (10404-816+64)= (110)(9652)=1061720

Answer:1023+ 83=1,061,7đôi mươi.

Example 2:Factorize the expression 8x3+ 27 by using the a^3+b^3 formula.

Solution:To factorize:8x3+ 27.We will use thea3+ b3formula to factorize this.We can write the given expression as8x3+ 27 = (2x)3+ 33We will substitute a = 2x and b = 3 in the formula ofa3+ b3.a3+ b3= (a + b) (a2- ab + b2)(2x)3+33=(2x+3)((2x)2-(2x)(3)+32)= (2x+3) (4x2-6x+9)

Answer:8x3+ 27= (2x + 3) (4x2-6x + 9).

Example 3: Simplify 193 + 203 using a cube plus b cubeformula

Solution: To find193 + 203

Let us assume a = 19 & b = 20Using formulaa3+ b3= (a + b) (a2- ab + b2)We will substitute these in thea3+ b3formulaa3+ b3= (a +b) (a2- ab + b2)193+203= (19+20)(192-(19)(20)+202)= (39)(361-380+400)= (39)(381)= 14,859Answer:193+203= 14859.

FAQs on a^3+b^3Formula

What Is the Expansion of a3 + b3 Formula?

a3+b3formula is read as a cube plus b cube. Itis called the sum of cubes (of two numbers) formula. Its expansion is expressed asa3+b3= (a +b) (a2- ab + b2)

What Is thea3+b3 Formula in Algebra?

The a3+b3formula is one of the important algebraic identiy. It is read as a cube plus b cube. Its a3+b3formula is expressed asa3+b3= (a +b) (a2-ab + b2)

How To Simplify Numbers Usingthea3+b3 Formula?

Let us understand the use of the a3+b3formula with the help of the following example.Example: Find the value of 103+ 23using the a3+b3formula.To find:103+23Let us assume that a = 10and b = 2.We will substitute these in the formula ofa3+ b3.a3+ b3= (a +b) (a2- ab + b2)103+23= (10+2)(102-(10)(2)+22)= (12) (100-20+4)= (12)(84)= 1008Answer:103+23= 1008.

How To Use thea3+b3 Formula Give sầu Steps?

The following steps are followed while usinga3+b3formula.

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Firstlyobserve sầu the pattern of the two numbers whether thenumbers have sầu ^3 as power or not.Write down the formula ofa3+ b3 = (a +b) (a2-ab + b2)Substitute the values of a and b in thea3+b3formula.Multiply a và b separatelywith(a2- ab + b2)and simplify.