p^6 512q^6 =(p^2)^3 (8q^2)^3 =(p^2 8q^2)[(p^2)^2+p^2× 8q^2+(8q^2)^2) =(p^2 8q^2)(p^4+8p^2q^2+64q^4) ...

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Algebraic Identities

Factorize : ...

Question

Factorize :
$p^{6} - 512 q^{6}$

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Solution

$p^{6} - 512 q^{6}$
$= (p^{2})^{3} - (8 q^{2})^{3}$
$= (p^{2} - 8 q^{2}) [(p^{2})^{2} + p^{2} \times 8 q^{2} + (8 q^{2})^{2})$
$= (p^{2} - 8 q^{2}) (p^{4} + 8 p^{2} q^{2} + 64 q^{4})$

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