How do you factor #a^3 - (a-4)^3#?
1 Answer
Feb 15, 2016
Explanation:
This is a difference of cubes, which factors into:
#x^3-y^3=(x-y)(x^2+xy+y^2)#
Here, we have
#a^3-(a-4)^3#
#=(a-(a-4))(a^2+a(a-4)+(a-4)^2)#
We can continue to simplify.
#=(a-a+4)(a^2+a^2-4a+a^2-8a+16)#
#=4(3a^2-12a+16)#
This cannot be factored further (without the help of complex numbers).