Question

सरळरूप द्या.

(4a − 3)³ − (4a + 3)³

Answer 1

आपल्याला ठाऊक आहे कि, 

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

\[\ \left(4a - 3 \right)^3 - \left(4a + 3 \right)^3 \] 

\[ =  \left(4a \right)^3 - \left(3 \right)^3 - 3 \times  \left(4a \right)^2  \times 3 + 3 \times 4a \times  \left(3 \right)^2 - \left\{\left(4a \right)^3 + \left(3 \right)^3 + 3 \times \left( 4a \right)^2 \times 3 + 3 \times 4a \times \left(3 \right)^2 \right\}\]

\[= 64 a^3 - 27 - 144 a^2  + 108 - 64 a^3 - 27 - 144 a^2 - 108\]

\[= -288 a^2 - 54\]