Question

Which of the following shows the general formula for factoring the difference of cubes?

O (a - b)(a? - ab – b?)
O (a + b)(a² + ab + b2)
O (a + b)(a? - ab + b)
O (a - b)(a² + ab + b)

Answer 1

(a - b)(a² + ab + b²)

Explanation:

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Answer 2

(a - b)(a² + ab + b²)

Explanation:

The difference of cubes is expressed as:

a³-b³

Using trial and error:

a³-b³

Check (a - b)(a² + ab + b²)

Expand

(a - b)(a² + ab + b²)

= a(a²)+a(ab)+a(b²)-a²b-ab²-b³

= a³+a²b+a(b²)-a²b-ab²-b³

Collect the like terms

= a³+a²b-a²b+ab²-ab²-b³

= a³-b³

Hence the required option is