JAMB 2010 · UTME · Q14

If $9x^2 + 6xy + 4y^2$ is a factor of $27x^3 - 8y^3$ , find the other factor.

Worked solution (try it first)

Both terms are cubes: $27x^3 = (3x)^3$ and $8y^3 = (2y)^3$ .
A difference of cubes factorises as $A^3 - B^3 = (A - B)(A^2 + AB + B^2)$ .
With $A = 3x$ and $B = 2y$ : $(3x - 2y)(9x^2 + 6xy + 4y^2)$ .
The other factor is $3x - 2y$ , option A.

Report a problem with this question