Question

find the value of 64x^3-125y^3,if 4x-5y=16 and xy=12

Answer 1

your answer for above question

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