How do you factor # 8x^3 - 216#?

1 Answer
Jun 24, 2016

Answer:

#8(x-3)(x^2+3x+9)#

Explanation:

First step is to 'take out' a common factor of 8.

#rArr8(x^3-27)........ (A)#

now #x^3-27" is a " color(blue)"difference of cubes"# and is factorised as shown.

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

#x^3=(x)^3" and " 27=(3)^3#

hence a = x and b = 3

#rArrx^3-27=(x-3)(x^2+3x+3^2)=(x-3)(x^2+3x+9)#

Substituting this back into (A)

#rArr8x^3-216=8(x-3)(x^2+3x+9)#