Question

If x-2y=8 and xy=6 find the value of x^3-8y^3

Answer 1

x3 + 8y3

= x3 + (23)y3

= x3 + (2y)3

= [x+2y] [x2 - x(2y) + (2y)2] [Using: a3+b3 = (a+b)(a2-ab+b2)]

= 10 [x2 - 2xy + (2y)2] [Given: x+2y=10]

= 10 [x2 - (6xy-4xy) + (2y)2]

= 10 [x2 - 6xy + 4xy + (2y)2]

= 10 [(x2 + 4xy + (2y)2) - 6xy]

= 10 [ (x2 + 2*x(2y) + (2y)2) - 6xy ]

= 10 [ (x+2y)2 - 6xy ]

= 10 [102 - 6*15] [Given: x+2y=10 and xy=15]

= 10 [100 - 90]

= 10 * 10

= 100

Answer 2

Hope this ans helps u

x3 + 8y3

= x3 + (23)y3

= x3 + (2y)3

= [x+2y] [x2 - x(2y) + (2y)2] [Using: a3+b3 = (a+b)(a2-ab+b2)]

= 10 [x2 - 2xy + (2y)2] [Given: x+2y=10]

= 10 [x2 - (6xy-4xy) + (2y)2]

= 10 [x2 - 6xy + 4xy + (2y)2]

= 10 [(x2 + 4xy + (2y)2) - 6xy]

= 10 [ (x2 + 2*x(2y) + (2y)2) - 6xy ]

= 10 [ (x+2y)2 - 6xy ]

= 10 [102 - 6*15] [Given: x+2y=10 and xy=15]

= 10 [100 - 90]

= 10 * 10

= 1008