Question

Write the factors of
`{a}^(3) + {b}^(3) .`​

Answer 1

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

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) )`

`\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto`

`\textsl{OAmalOHopeO}`

Answer 2

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) ) / (a + b)`

We get

a quotient of

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

So our factors are

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