Question

find
the value of 64xcube--125ycube iif 4x-5y=16 annd xy=12

Answer 1

Answer:

11712

Step-by-step explanation:

64x³ - 125y³

= (4x)³ - (5y)³

a³-b³ = (a-b)(a²+b²+ab)

a³-b³ = (a-b)( (a-b)²+3ab)

a = 4x & b = 5y

(4x-5y)( (4x-5y)² + 3(4x)(5y) )

= 16 (  16² + 60xy )

= 16 ( 256 + 60*12)

= 12 (256 + 720)

= 12 * 976

= 11712

Answer 2

Answer:

$64x^3-125y^3=15616$

Step-by-step explanation:

Given :

$4x-5y=16$ and $xy=12$

To find :

The value of $64x^3-125y^3$

Solution :

To get the value,

Consider $4x-5y=16$

Cube both sides,

$(4x-5y)^3=(16)^3$

$(4x)^3+(-5y)^3+3(4x)^2(-5y)+3(4x)(-5y)^2=(16)^3$

$64x^3-125y^3-240x^2y+300xy^2=4096$

$64x^3-125y^3-60xy(4x-5y)=4096$

$64x^3-125y^3-60(12)(16)=4096$

$64x^3-125y^3-11520=4096$

$64x^3-125y^3=15616$

Therefore, The required result is

$64x^3-125y^3=15616$