Factorise (x6/343) + (343/x6)

(x⁶/343) + (343/x⁶)

Above terms can be written as,

(x²/7)³ + (7/x²)³

We know that, a³ + b³ = (a + b) (a² – ab + b²)

Where, a = (x²/7), b = (7/x²)

Then, (x²/7)³ + (7/x²)³ = [(x²/7) + (7/x²)] [(x²/7)² – ((x²/7) × (7/x²)) + (7/x²)²]

= [(x²/7) + (7/x²)] [(x⁴/49) – 1 + (49/x⁴)]

(ii)8x³ – 1/27y³

Above terms can be written as,

(2x)³ – (1/3y)³

We know that, a³ – b³ = (a – b) (a² + ab + b²)

Where, a = 2x, b = (1/3y)

Then, (2x)³ – (1/3y)³ = (2x – (1/3y)) ((2x)² + (2x × (1/3y)) + (3y)²)

= (2x – (1/3y)) (4x² + (2x/3y) + 9y²)

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