Question

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

Answer 1

Answer:

Answer

4x−5y=16

Cubing on both sides

⇒(4x−5y)

3

=(16)

3

⇒64x

3

−125y

3

−3×4x×5y(4x−5y)=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

Answer 2

Answer:

64x³ - 125y³ = (4x-5y)³ + 3(4x)(5y)(4x-5y)

= (16)³ + 3(4)(5)(12)(16)

= 4096 + 11520

= 15616.