How do you factor #8x^3 - 1000#?
1 Answer
Apr 29, 2016
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)#