Question

Simplify.

(3r − 2k)³ + (3r + 2k)³

Answer 1

It is known that,

\[\left( a + b \right)^3 = a^3 + b^3 + 3 a^2 b + 3a b^2 ; \left( a - b \right)^3 = a^3 - b^3 - 3 a^2 b + 3a b^2\]

\[\left( 3r - 2k \right)^3 + \left( 3r + 2k \right)^3 \]

\[ = \left( 3r \right)^3 - \left( 2k \right)^3 - 3 \times \left( 3r \right)^2 \times 2k + 3 \times 3r \times \left( 2k \right)^2 + \left( 3r \right)^3 + \left( 2k \right)^3 + 3 \times \left( 3r \right)^2 \times 2k + 3 \times 3r \times \left( 2k \right)^2 \]

\[ = 27 r^3 - 8 k^3 - 54 r^2 k + 36r k^2 + 27 r^3 + 8 k^3 + 54 r^2 k + 36r k^2 \]

\[ = 54 r^3 + 72r k^2\]