How do you factor #27x³ - 64y³#?

1 Answer
Jan 31, 2016

Answer:

# (3x - 4y )(9x^2 + 12xy +16y^2 ) #

Explanation:

This is a difference of 2 cubes which can be factorised as

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

for # 27x^3 - 64y^3 , a = 3x color(black)(" and ") b = 4y #

substituting these into the above expression to obtain

# 27x^3 - 64y^3 = (3x - 4y )( 9x^2 + 12xy + 16y^2 ) #