Factoring Sums or Differences of Cubes

Question

m³+125

 

Factor completely

Answer 1

First, it is important to identify what you will be using. It is a sum. Each term is a cube. So, it's a sum of cubes.

 

Second, break out the formula for a sum of cubes. It's similar to a difference of cubes except the signs are different. A³ + B³=(A+B)(A²-AB+B²). I remember the signs with SOAP (Same, Opposite, Always positive).

 

Third, apply the formula. m³= A³ , so A=m, and 125=B³, so B=5. You can take the cube root of each to find these. Now just plug A and B in.

 

m³+125=(m+5)(m²-5m+25)

 

Done

Answer 2

Hi Ruby,

 

This is sum of cubes. (a + b) (a² -ab + b²)

 

(m + 5) (m² -5m +25).  That's it.