Check the solution to "What is the formula for a3-b3?"

Presley Schroeder

Answered question

2022-12-14

What is the formula for

(a^{3} - b^{3})

Hector Key

Beginner2022-12-15Added 1 answers

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

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

a b - a c = a (b - c)

and

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

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

Answer is

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

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