What is the difference between `(a+b)^3 and a^3 + b^3`   Explain the difference between (a+b)^3 AND a^3+b^3

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sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to expand the cube of a+b such that:

`(a+b)^3 = a^3 + b^3 + 3ab(a+b)`

You should evaluate the requested difference between `(a+b)^3 ` and `a^3 + b^3` , hence, you need to subtract `a^3 + b^3`  such that:

`(a+b)^3 - a^3- b^3 = a^3 + b^3- a^3 - b^3 + 3ab(a+b)`

Reducing like terms yields:

`(a+b)^3 - a^3 - b^3 = 3ab(a+b)`

Hence, evaluating the difference between `(a+b)^3`  and `a^3 + b^3`  yields `(a+b)^3 - a^3 - b^3 = 3ab(a+b).`

durbanville's profile pic

durbanville | High School Teacher | (Level 2) Educator Emeritus

Posted on

    

Simplify them to understand them:

`(a+b)^3 = (a+b)(a+b)(a+b)`

When expanded it looks like this:

`(a+b)(a^2 + 2ab + b^2)'`

Expanded fully:

`a^3 + 2a^2b + ab^2 + a^2b +2ab^2 + b^3` 

=`a^3 + 3a^2b+3ab^2 + b^3`

Notice the difference with the other expression

 `a^3 +b^3`

` = a.a.a+ b.b.b`

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powerrangerpink's profile pic

powerrangerpink | Student, Grade 11 | (Level 1) eNoter

Posted on

( a+b ) ^ 3 means (a+b)x (a+b)x( a+b) .

a^3 + b^ 3 means (axaxa) + (bxbxb).

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