How do you factor $8m³ - 27n³$ ?

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Answer 1 · 2016-01-23T16:36:38

$(2m-3n)(4m^2+6mn+9n^2)$

Both of these terms are cubed term:

Because of this, this expression is a difference of cubes.

This is a fairly common pattern that can be factored as

$a^3-b^3=(a-b)(a^2+ab+b^2)$

Since $8m^3-27n^3$ can be expressed as $(2m)^3-(3n)^3$ , we can factor this as if $a=2m$ and $b=3n$ .

$8m^3-27n^3$

$=(2m)^3-(3n)^3$

$=(2m-3n)((2m)^2+2m(3n)+(3n)^2)$

$=(2m-3n)(4m^2+6mn+9n^2)$

How do you factor 8m³ - 27n³8m³ - 27n³?