The shortest form of ( a 3 + b 3 ) ( a 2 − a b + b 2 ) is ___

The algebraic fraction is assumed to be: ( a 3 + b 3 ) ( a 2 − a b + b 2 ) Here, we can pursue the following identities: ( a 3 + b 3 ) = ( a + b ) ( a 2 − a b + b 2 ) ⇒ The term ( a 2 − a b + b 2 ) is common for numerator and denominator as well. Thus, we can strike off the common term. ⇒ The lowest form is: a+b

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High School
Algebra
Pre-Algebra
Fractions

Heidy Haley

Answered question

2023-02-08

The shortest form of

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

is ___

Answer & Explanation

Lavaroniuve

Beginner2023-02-09Added 6 answers

The algebraic fraction is assumed to be:

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

Here, we can pursue the following identities:

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

\Rightarrow

The term

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

is common for numerator and denominator as well. Thus, we can strike off the common term.

\Rightarrow

The lowest form is: a+b

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