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Types of Expressions Based on the Number of Terms

Solve : 3x+...

Question

Solve : $(3 x + 7 y)^{3} + (3 x - 7 y)^{3}$

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Solution

A] $(3 x + 7 y)^{3} + (3 x - 7 y)^{3}$
as $(a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b)$
$(a - b)^{3} = a^{3} + b^{3} - 3 a b (a - b)$
$= (3 x)^{3} + (7 y)^{3} + 3 \times 3 x \times 7 y (3 x + 7 y) + (3 x)^{3} + (7 y)^{3} - 3 \times 3 x \times 7 y (3 x - 7 y)$
= $27 x^{3} + 343 y^{3} + 63 x y (3 x + 7 y) + 27 x^{3} + 343 y^{3} - 63 x y (3 x - 7 y)$
= $54 x^{3} + 686 y^{3} + 189 x^{2} y + 441 x y^{2} - 189 x^{2} y + 441 x y^{2}$
= $54 x^{3} + 686 y^{3} + 882 x y^{2}$

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