Question

Find the value of 125x³ - 8y³ . If 5x - 2y = 6 and xy = 4 . Explain it in detail .

Answer 1

${(5x - 2y)}^{2} = {6}^{2} \\ {25x}^{2} + {4y}^{2} - 20xy = 36 \\ {25x}^{2} + {4y}^{2} - 20 \times 4 = 36 \\ {25x}^{2} + {4y}^{2} = 36 + 80 = 116$
${125x}^{ 3} - {8y}^{3} = \\ (5x - 2y)( {25x}^{2} + {4y}^{2} + 10xy)$
6×(116+10×4)
6×156=936

Answer 2

hey mate!

125x³ - 8y³

= (5x)³ - (2y)³. (since, a³ - b³= (a-b)(a²+ab +b²))

= (5x -2y ){(5x)² + (5x)(2y) + (2y)²}

= 6 { 25x² +10xy + 4y²}

= 6(25x²+4y² +10(4) )

= 6 ( 116+40) (after doing square of 5x -2y, we get 116)

= 6 * 156

= 936

hope it was helpful!!