How do you factor #8x^3 - 1000#?

1 Answer
Apr 29, 2016

Answer:

#8(x-5)(x^2+5x+25)#

Explanation:

The first step is to 'take out' common factor of 8

#rArr 8x^3-1000 = 8(x^3-125)#

now # x^3-125color(blue)" is a difference of cubes "#

and is factorised as follows :

#color(red)(|bar(ul(color(white)(a/a)color(black)( a^3-b^3 = (a-b)(a^2+ab+b^2))|)))#

now # x^3=(x)^3" and " 125=(5)^3#

for factorising purposes: a = x and b = 5

#rArr x^3-125=(x-5)(x^2+5x+25)#

#rArr 8x^3-1000=8(x-5)(x^2+5x+25)#