# How do you factor #16x^3 - 250#?

##### 1 Answer

Sep 27, 2015

Separate out the common scalar factor

#16x^3-250 = 2(2x-5)(4x^2+10x+25)#

#### Explanation:

Both

#16x^3-250 = 2(8x^3-125)#

Now

So we find:

#2(8x^3-125)#

#=2((2x)^3-5^3)#

#=2(2x-5)((2x)^2+(2x)*5+5^2)#

#=2(2x-5)(4x^2+10x+25)#

...using the difference of cubes identity:

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