Question

factorise 729x^3 - 512y^3​

Answer 1

$\huge\underline{\underline{\overline{\overline{\mid{\red{\mathbb{SoLuTiOn}}}\mid}}}}$

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$\longmapsto\large\underline{\red{729x³ - 512y³}}$

$\longmapsto\large{\pink{= 9³x³ - 8³y³}}$

$\longmapsto\large{\green{= (9x)³ - (8y)³}}$

$\longmapsto{\orange{= (9x - 8y) [ (9x)² + (8y)² + (9x)×(8y) ]}}$

$\longmapsto\large{\purple{=(9x - 8y)( 81x² + 64y² + 72xy)}}$

$\large{\tt{Identity\:used\::}}$

$\large{\tt{\blue{(a³ - b³) = (a - b) (a² + b² + ab).}}}$

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Answer 2

Answer:

⟼ 729x³−512y³

⟼=9³x³−8³y³

⟼=(9x)³−(8y)³

⟼=(9x−8y)[(9x)²+(8y)²+(9x)×(8y)]

⟼=(9x−8y)(81x²+64y²+72xy)

⟼=(9x−8y)(81x²+64y²+72xy

(a³−b³)=(a−b)(a²+b²+ab).

Step-by-step explanation:

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