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Question
Simplify.
(5x − 7y)3 + (5x + 7y)3
Solution
It is known that,
\[\left( a + b \right)^3 = a^3 + b^3 + 3 a^2 b + 3a b^2 ; \left( a - b \right)^3 = a^3 - b^3 - 3 a^2 b + 3a b^2\]
\[\ \left( 5x - 7y \right)^3 + \left( 5x + 7y \right)^3 \]
\[ = \left( 5x \right)^3 - \left( 7y \right)^3 - 3 \times \left( 5x \right)^2 \times 7y + 3 \times 5x \times \left( 7y \right)^2 + \left( 5x \right)^3 + \left( 7y \right)^3 + 3 \times \left( 5x \right)^2 \times \left( 7y \right) + 3 \times 5x \times \left( 7y \right)^2 \]
\[ = 125 x^3 - 343 y^3 - 525 x^2 y + 735x y^2 + 125 x^3 + 343 y^3 + 525 x^2 y + 735x y^2 \]
\[ = 250 x^3 + 1470x y^2\]
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