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Algebraic Identities

Simplify: 5...

Question

Simplify: $(5 - 2 x)^{3} - (5 + 2 x)^{3}$

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Solution

$(5 - 2 x)^{3} - (5 + 2 x)^{3}$
Using, $(a^{3} - b^{3}) = (a - b) (a^{2} + a b + b^{2})$
$= (5 - 2 x - 5 - 2 x) [(5 - 2 x)^{2} + (5 + 2 x)^{2} + (5 - 2 x) (5 + 2 x)]$
$= (- 4 x) [(25 + 4 x^{2} - 10 x) + (25 + 4 x^{2} + 10 x) + 25 - 4 x^{2}]$
$= (- 4 x) (75 + 4 x^{2})$

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\frac{49 (x^{4} - 2 x^{3} - 15 x^{2})}{14 x (x - 5)}

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(2 x^{3} + 4) \div 2

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