Question

How do you factor `8m^3 - 125n^3`?

Answer 1

`(2m-5n)(4m^2+10mn+25n^2)`

Explanation:

`"this is a "color(blue)"difference of cubes"`

`"and factors in general as"`

`•color(white)(x)a^3-b^3=(a-b)(a^2+ab+b^2)`

`8m^3=(2m)^3rArra=2m`

`125n^3=(5n)^3rArrb=5n`

`8m^3-125n^3=(2m-5n)((2m)^2+(2mxx5n)+(5n)^2)`

`color(white)(xxxxxxxxx)=(2m-5n)(4m^2+10mn+25n^2)`

Answer 2

`(2m-5n) (4m^2 + 10mn + 25n^2)`

Explanation:

Remember that `a^3-b^3=(a-b)(a^2+ab+b^2)`

`8m^3-125n^3=2^3m^3-5^3n^3=(2m)^3-(5n)^3`

Therefore, `a=2m, b=5n`

Sub in: `(2m-5n) (4m^2 + 10mn + 25n^2)`