Question

The polynomial is missing the coefficient of the third and last terms.

8x³ - 144x²y + __xy²-__y^3
In order to be factorable using the binomial theorem, the coefficient of xy² is
and the coefficient of y3 is __

Answer 1

coefficient of xy^2 is : 864 and that of y^3 is 1728

Explanation:

Using binomial theorem,

1st term is 1 (ax)^3 = 8x^3 from which a = 2

2nd term is 3(ax)^2(by) = -144x^2y from which b = -12

3rd term is 3(ax)(by)^2 = 3(2x)(-12y)^2 = 864

4th term is 1(by)^3 = 1(-12y)^3 = -1728y^3