Question

Write the factors of e=" {a}^{3} + {b}^{3} ." alt=" {a}^{3} + {b}^{3} ." align="absmiddle" class="latex-formula">​

Answer 1

Step-by-step explanation:

$a {}^{3} + b {}^{3}$

Notice how that for both a and b are raised to an odd power. This means we can factor this by a binomial raised to an odd power.

Let divide this by

$a + b$

Since that is also a odd power.

$( {a}^{3} + {b}^{3} ) \div (a + b)$

We get

a quotient of

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

So our factors are

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

Answer 2

Answer:

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

Step-by-step explanation:

$\textbf{We need to factor this expression}$ $\textbf{by applying the sum of two cubes rule:}$

$\Longrightarrow$ $A^{3} +B^{3} =(A+B)(A^{2} -AB+B^{2} )$

Here,  

A= a

B= b

So, $(a+b)(a^{2} -ab+b^{2} )$

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