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Addition of Polynomials

2 x-3 y3+x+3 ...

Question

$(2 x - 3 y)^{3} + (x + 3 y)^{3} + 3 (2 x - 3 y)^{2} (x + 3 y) + 3 (2 x - 3 y) (x + 3 y)^{2} =$

A

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B

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C

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D

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Solution

The correct option is A
Substitute $2 x - 3 y = a$ and $(x + 3 y) = b$
$\Rightarrow (2 x - 3 y)^{3} + (x + 3 y)^{3} + 3 (2 x - 3 y)^{2} (x + 3 y) + 3 (2 x - 3 y) (x + 3 y)^{2}$
$= a^{3} + b^{3} + 3 a^{2} b + 3 a b^{2}$
$= (a + b)^{3}$
$= (2 x - 3 y + x + 3 y)^{3}$
$= (3 x)^{3}$
$= 27 x^{3}$

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Similar questions

Q. The expression

(2 x - 3 y)^{3} + (x + 3 y)^{3} + 3 (2 x - 3 y)^{2} (x + 3 y) + 3 (2 x - 3 y) (x + 3 y)^{2} =

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(2 x - 3 y)^{3} + (x + 3 y)^{3} + 3 (2 x - 3 y)^{2} (x + 3 y) + 3 (2 x - 3 y) (x + 3 y)^{2}

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