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Write the factors of [tex] {a}^{3} + {b}^{3} .[/tex]​

Sagot :

Step-by-step explanation:

[tex]a {}^{3} + b {}^{3} [/tex]

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

[tex]a + b[/tex]

Since that is also a odd power.

[tex]( {a}^{3} + {b}^{3} ) \div (a + b)[/tex]

We get

a quotient of

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

So our factors are

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

Answer:

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

Step-by-step explanation:

[tex]\textbf{We need to factor this expression}[/tex] [tex]\textbf{by applying the sum of two cubes rule:}[/tex]

[tex]\Longrightarrow[/tex] [tex]A^{3} +B^{3} =(A+B)(A^{2} -AB+B^{2} )[/tex]

Here,  

A= a

B= b

So, [tex](a+b)(a^{2} -ab+b^{2} )[/tex]

[tex]\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto[/tex]

[tex]\textsl{OAmalOHopeO}[/tex]