Question

Expess16x^4-96x^3y+216x^2y^2-216xy^3+81y^4 in the form (ax+by)^n ???

Answer 1

Hint: \[(a x+b y)^4=a^4 x^4+4 a^3 b x^3 y+6 a^2 b^2 x^2 y^2+4 a b^3 x y^3+b^4 y^4 \]

Answer 2

Thamk you @robtobey Im not sure what your doing here though.

Answer 3

@robtobey could you please explain the process for me? I don't want solution, would like to know how the steps to get there.

Answer 4

\[16 x^4-96 x^3 y+216 x^2 y^2-216 \text{xy}^3+81 y^4\]\[a^4 x^4+4 a^3 b x^3 y+6 a^2 b^2 x^2 y^2+4 a b^3 x y^3+b^4 y^4 \]Compare the first terms. a^4 = 16, a = 2
Using the same approach on the last terms, b^4 = 81, b = 3

\[(2 x+3 y)^4=16 x^4+96 x^3 y+216 x^2 y^2+216 x y^3+81 y^4 \]