Question

Find the value of x^3+y^3-12xy +64 whenx+y=-4

Answer 1

x^3 +y^3 - 12xy + 64 
= x^3 + y^3 + 64 - 3(4xy) => Notice that the polynomial is in the form of: 
a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ac) 
therefore it factors as: 
x^3 + y^3 + 64 - 12xy 
= (x + y + 4)(x^2 + y^2 + 16 - xy - 4y - 4x) => substitute for x + y = -4 
= (-4 + 4)(x^2 + y^2 + 16 - xy - 4y - 4x) 
= 0 * (x^2 + y^2 + 16 - xy - 4y - 4x) 
= 0