How do you factor #54x^3-16y^3#?

1 Answer
Mar 26, 2016

Answer:

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

Explanation:

There is a common factor of 2 , thus

#= 2(27x^3 - 8y^3) #

Now # 27x^3 - 8y^3 " is a difference of cubes " #

which factors as follows:

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

For # 27x^3 , a = 3x " and for " 8y^3 , b = 2y #

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

#rArr 54x^3-16y^3 = 2(3x-2y)(9x^2+6xy+4y^2) #