Question

Given (1) 2x - 5y= 18 and (ii) xy = 15 then find the value of 8x3 - 125y3.
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Answer 1

Finding values

Given: 2x - 5y = 18, xy = 15

To find: the value of 8x³ - 125y³

Solution:

We must know that,

a³ - b³ = (a - b) (a² + b² + ab)

a² + b² = (a - b)² + 2ab

Now, 8x³ - 125y³

= (2x)³ - (5y)³

= (2x - 5y) {(2x)² + (5y)² + 2x * 5y}

= (2x - 5y) {(2x - 5y)² + 2 * 2x * 5y + 2x * 5y}

= (2x - 5y) {(2x - 5y)² + 30 xy}

= 18 (18² + 30 * 15)

= 18 (324 + 450)

= 18 * 774

= 13932

Answer: 8x³ - 125y³ = 13932