Question : The simplified form of $(x+2y)^3 + (x-2y)^3$ is:
Option 1: $2x^3+24xy^2$
Option 2: $2x^3-24xy^2$
Option 3: $x^3-8y^3$
Option 4: $x^3+8y^3$
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Correct Answer: $2x^3+24xy^2$
Solution :
Given: $(x+2y)^3 + (x-2y)^3$
$=x^3+(2y)^3+3(x)(2y)(x+2y)+x^3-(2y)^3-3(x)(2y)(x-2y)$
$=2x^3+6xy(x+2y)-6xy(x-2y)$
$=2x^3+6xy(x+2y-(x-2y))$
$=2x^3+6xy(x+2y-x+2y)$
$=2x^3+6xy(4y)$
$=2x^3+24xy^2$
Hence, the correct answer is $2x^3+24xy^2$.
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