Question

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

Answer 1

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,

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

Answer 2

Answer:

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

Step-by-step explanation: