Find the value

Question:

Find the value

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

 

Solution:

$=(x+2+x-2)\left((x+2)^{2}-(x+2)(x-2)+(x-2)^{2}\right)$

$\therefore\left[a^{3}+b^{3}=(a+b)\left(a^{2}-a b+b^{2}\right)\right]$

$=2 x\left(x^{2}+4 x+4-(x+2)(x-2)+x^{2}-4 x+4\right)$

$=2 x\left(2 x^{2}+8-\left(x^{2}-2^{2}\right)\right)$

$\left[\therefore(a+b)(a-b)=a^{2}-b^{2}\right]$

$=2 x\left(2 x^{2}+8-x^{2}+4\right)$

$=2 x\left(x^{2}+12\right)$

$\therefore(x+2)^{3}+(x-2)^{3}=2 x\left(x^{2}+12\right)$

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