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Which of the following expressions is equivalent to a3 + b3?

(a - b)(a2 + ab + b2)
a3 + a2b + ab2 - a2b - ab2 - b3
(a + b)(a2 - ab + b2 )
(a + b)(a3 + b3)

~all the big numbers next to the variables are the exponent example, b2 ; b^2

Respuesta :

kudzordzifrancis
ANSWER
[tex] {a}^{3} + {b}^{3} = (a + b)( {a}^{2 } - ab + {b}^{2} )[/tex]


EXPLANATION

To find the expression that is equivalent to
[tex]{a}^{3} + {b}^{3}[/tex]
we must first expand
[tex] {(a + b)}^{3} [/tex]
Then we rearrange to find the required expression.


So let's get started.


[tex] {(a + b)}^{3} = (a + b) {(a + b)}^{2} [/tex]

We expand the parenthesis on the right hand side to get,



[tex] {(a + b)}^{3} = (a + b) ( {a}^{2} + 2ab + {b}^{2} )[/tex]



We expand again to obtain,

[tex] {(a + b)}^{3} = {a}^{3} + 3 {a}^{2}b + 3a {b}^{2} + {b}^{3} [/tex]


Let us group the cubed terms on the right hand side to get,

[tex] {(a + b)}^{3} = {a}^{3} + {b}^{3} + 3 {a}^{2}b + 3a {b}^{2} [/tex]




[tex] {(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab (a+ b)[/tex]





We make the cubed terms the subject,

[tex] {(a + b)}^{3} - 3ab (a+ b) = {a}^{3} + {b}^{3} [/tex]

We factor to get,


[tex] (a + b)({(a + b)}^{2} - 3ab ) = {a}^{3} + {b}^{3} [/tex]


We expand the bracket on the left hand side to get,

[tex] (a + b)( {a}^{2} + 2ab + {b}^{2} - 3ab ) = {a}^{3} + {b}^{3} [/tex]


We finally simplify to get,

[tex] (a + b)( {a}^{2} - ab + {b}^{2} ) = {a}^{3} + {b}^{3} [/tex]
MrRoyal

Equivalent equations are equations with the same values

The equivalent expression of a^3  + b^3 is (a + b)(a^2 -ab + b^2)

The expression is given as:

a^3 + b^3

The above expression represents the sum of cube

Using the equation of the sum of cubes, we have:

a^3  + b^3 = (a + b)(a^2 -ab + b^2)

Hence, the equivalent expression of a^3  + b^3 is (a + b)(a^2 -ab + b^2)

Read more about equivalent expression at:

https://brainly.com/question/2972832

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