How do you factor #b^3-64c^3#?

2 Answers
Jan 1, 2016

Answer:

Apply the difference of cubes formula to see that
#b^3-64c^3= (b - 4c)(b^2 + 4bc + 16c^2)#

Explanation:

The difference of cubes formula states that

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

(Verify this by multiplying out the right hand side)

Then, for the given expression, we have

#b^3-64c^3 = b^3-(4c)^3 = (b - 4c)(b^2 + 4bc + 16c^2)#

Jan 1, 2016

Answer:

#b^3-64c^3=(b-4c)(b^2+4bc+16c^2)#

Explanation:

#b^3-64c^3# is a difference of cubes . The formula for factoring a difference of cubes is #(a-b)(a^2+ab+b^2)#, where #a=b# and #b=4c# in this case.

Substitute the values for #a and b# into the equation.

#(b-4c)(b^2+bxx4c+(4c)^2)#

Simplify.

#(b-4c)(b^2+4bc+16c^2)#