Question
Factorize the following expressions: $(x + 2)^3 + (x - 2)^3$
✓
Answer
$=(x+2+x-2)((x+2)^2-(x+2)(x-2)+(x-2)^2)[\therefore[a^3+b^3=(a+b)(a^2-a b+b^2)]$
$=2 x(x^2+4 x+4-(x+2)(x-2)+x^2-4 x+..4)$
$=2 x(2 x^2+8-(x^2-2^2))[\therefore(a+b)(a-b)=a^2-b^2]$
$=2 x(2 x^2+8-x^2+4)=2 x(x^2+12)$
$\therefore(x+2)^3+(x-2)^3=2 x(x^2+12)$
$=2 x(x^2+4 x+4-(x+2)(x-2)+x^2-4 x+..4)$
$=2 x(2 x^2+8-(x^2-2^2))[\therefore(a+b)(a-b)=a^2-b^2]$
$=2 x(2 x^2+8-x^2+4)=2 x(x^2+12)$
$\therefore(x+2)^3+(x-2)^3=2 x(x^2+12)$
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