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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

Verified Answer :

kudzordzifrancis

ANSWER
\({a}^{3} + {b}^{3} = (a + b)( {a}^{2 } - ab + {b}^{2} )\)


EXPLANATION

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


So let's get started.


\({(a + b)}^{3} = (a + b) {(a + b)}^{2}\)

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



\({(a + b)}^{3} = (a + b) ( {a}^{2} + 2ab + {b}^{2} )\)



We expand again to obtain,

\({(a + b)}^{3} = {a}^{3} + 3 {a}^{2}b + 3a {b}^{2} + {b}^{3}\)


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

\({(a + b)}^{3} = {a}^{3} + {b}^{3} + 3 {a}^{2}b + 3a {b}^{2}\)




\({(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab (a+ b)\)





We make the cubed terms the subject,

\({(a + b)}^{3} - 3ab (a+ b) = {a}^{3} + {b}^{3}\)

We factor to get,


\((a + b)({(a + b)}^{2} - 3ab ) = {a}^{3} + {b}^{3}\)


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

\((a + b)( {a}^{2} + 2ab + {b}^{2} - 3ab ) = {a}^{3} + {b}^{3}\)


We finally simplify to get,

\((a + b)( {a}^{2} - ab + {b}^{2} ) = {a}^{3} + {b}^{3}\)

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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