Factorization of x⁶ + 64y⁶
The polynomial \[ x^6+64y^6 \] on factorization gives ___________
Solution
\[ x^6+64y^6 \]
\[ =x^6+8x^3y^3+64y^6-8x^3y^3 \]
\[ =(x^3+4y^3)^2-(2\sqrt{2}xy^{3/2})^2 \]
\[ =(x^3-4x^2y+16xy^2-8y^3)(x^3+4x^2y+16xy^2+8y^3) \]
\[ \boxed{(x^2-2xy+4y^2)(x^4+2x^3y+4x^2y^2+8xy^3+16y^4)} \]