Question

2x-5y=10 and xy = 15. Find 8x³-125y³. Please help !

Answer 1

Step-by-step explanation:

${8x}^{3} - 125 {x}^{3} \\ = ( {2x})^{3} - ( {5y})^{3} \\ = (2x - 5y)(4 {x}^{2} + 10xy + 25 {y}^{2} ) \\ = 10(4 {x}^{2} + 150 + {25y}^{2} ) \\ = 40 {x}^{2} + 1500 + 250 {y}^{2}$

Answer 2

Sᴏʟᴜᴛɪᴏɴ :-

→ 2x - 5y = 10

Squaring both sides we get,

→ (2x - 5y)² = 10²

→ 4x² + 25y² - 20xy = 100

→ 4x² + 25y² = 100 + 20xy

Putting value of xy now,

→ 4x² + 25y² = 100 + 20*15

→ 4x² + 25y² = 100 + 300

→ 4x² + 25y² = 400 ------- Eqn(1)

Now,

using (a³ - b³) = (a - b)(a² + b² + ab) and a = 2x , b = 5y , we get,

→ {(2x)³ - (5y)³} = (2x - 5y)[(2x)² + (5y)² + 2x*5y]

→ (8x³ - 125y³) = (2x - 5y)(4x² + 25y² + 10xy)

Putting given values and value of Eqn(1) , Now,

→ (8x³ - 125y³) = 10 * (400 + 10*15)

→ (8x³ - 125y³) = 10 * (400 + 150)

→ (8x³ - 125y³) = 10 * 550

→ (8x³ - 125y³) = 5500 (Ans.)