How do you factor: #y= 8x^3 - 27 #?

1 Answer
May 1, 2016

Answer:

#(2x-3)(4x^2+6x+9)#

Explanation:

This expression is a#color(blue)" 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))color(white)(a/a)|)))#

now #8x^3=(2x)^3" and " 27=(3)^3#

For factorising purposes # a = 2x and b = 3#

#rArr 8x^3-27=(2x-3)(4x^2+6x+9)#