16a^3 128/b^3=2((2a)^3 (4b)^3) #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; =2[(2a 4/b)(4a^2+(4/b)^2+8a/b) ...

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Algebraic Identities

Solve: 16a3-...

Question

Solve:
$16 a^{3} - \frac{128}{b^{3}}$

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Solution

$16 a^{3} - \frac{128}{b^{3}} = 2 ((2 a)^{3} - (\frac{4}{b})^{3})$
$= 2 [(2 a - \frac{4}{b}) (4 a^{2} + (\frac{4}{b})^{2} + \frac{8 a}{b})]$

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