Question : Simplify: $(3x-2y)(3x+2y)(9x^2+4y^2)$
Option 1: $81x^4+16y^4$
Option 2: $81y^4-16x^4$
Option 3: $81y^4+16x^4$
Option 4: $81x^4-16y^4$
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Correct Answer: $81x^4-16y^4$
Solution :
Given: $(3x-2y)(3x+2y)(9x^2+4y^2)$
$=\{(3x)^2 - (2y)^2\} (9x^2+4y^2)$
$= (9x^2 - 4y^2)(9x^2+4y^2)$
$=(9x^2)^2 - (4y^2)^2 $
$= 81x^4 - 16y^4$
Hence, the correct answer is $81x^4 - 16y^4$.
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