Factoring?

[JSmith]

The question is: Factor 1331m³n⁹ - 125p⁶.

I have never factored an equation like this ... Help would be greatly appreciated!

Thanks!

 

[mmm4444bot]

Did you think about it? I'm guessing that your class is studying factoring patterns, like difference of squares, difference of cubes, sum of cubes, et cetera.

If so, then you should be thinking in terms of whether the given expression fits any of these patterns.

Inspect the powers and the coefficients (can they each be expressed as a square or cube of something?)

 

[Deleted member 4993]

The question is: Factor 1331m³n⁹ - 125p⁶.

I have never factored an equation like this ... Help would be greatly appreciated!

Thanks!

Hint:

a³- b³ = (a-b)(a² + ab + b²)

a² - b² = (a + b)(a - b)

 

[JSmith]

Hint:

a³- b³ = (a-b)(a² + ab + b²)

a² - b² = (a + b)(a - b)

Would this substitution be correct??

1331m³n⁹-125p⁶= (11mn³ - 5p²)(121m²n⁶ + 55mn³p² + 25p⁴)

 

[mmm4444bot]

[Is] this [factorization] correct?

1331m³n⁹-125p⁶ = (11mn³ - 5p²)(121m²n⁶ + 55mn³p² + 25p⁴)

Yes -- good job! :cool:

 

[JSmith]

Yes -- good job! :cool:

Thank you! Do I have to take this any further or is it fully factored?

 

[mmm4444bot]

is it fully factored?

Yes.

None of the basic factoring patterns can be further factored. If they could, why teach them? :cool:

 

[HallsofIvy]

Yes.

None of the basic factoring patterns can be further factored. If they could, why teach them? :cool:

Cannot be further factor with integer coefficients and exponents.