Question

सरळरूप द्या.

(5x − 7y)³ + (5x + 7y)³

Answer 1

आपल्याला ठाऊक आहे कि, 

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

\[\   \left( 5x - 7y \right)^3  +  \left( 5x + 7y \right)^3 \] 

\[ = \left( 5x \right)^3  -  \left( 7y \right)^3  - 3 \times  \left( 5x \right)^2  \times 7y + 3 \times 5x \times  \left( 7y \right)^2  +  \left( 5x \right)^3  +  \left( 7y \right)^3  + 3 \times  \left( 5x \right)^2  \times \left( 7y \right) + 3 \times 5x \times  \left( 7y \right)^2 \]

\[ = 125 x^3  - 343 y^3  - 525 x^2 y + 735x y^2  + 125 x^3  + 343 y^3  + 525 x^2 y + 735x y^2 \]

\[ = 250 x^3  + 1470x y^2\]