How do you factor #54x^3-16y^3#?
1 Answer
Mar 26, 2016
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) #