Question:
Find the value
$(x+2)^{3}+(x-2)^{3}$
Solution:
$=(x+2+x-2)\left((x+2)^{2}-(x+2)(x-2)+(x-2)^{2}\right)$
$\therefore\left[a^{3}+b^{3}=(a+b)\left(a^{2}-a b+b^{2}\right)\right]$
$=2 x\left(x^{2}+4 x+4-(x+2)(x-2)+x^{2}-4 x+4\right)$
$=2 x\left(2 x^{2}+8-\left(x^{2}-2^{2}\right)\right)$
$\left[\therefore(a+b)(a-b)=a^{2}-b^{2}\right]$
$=2 x\left(2 x^{2}+8-x^{2}+4\right)$
$=2 x\left(x^{2}+12\right)$
$\therefore(x+2)^{3}+(x-2)^{3}=2 x\left(x^{2}+12\right)$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.