Question:
If \[ x=3 \quad \text{and} \quad y=-1 \] find the value of:
\[ (9y^2 – 4x^2)(81y^4 + 36x^2y^2 + 16x^4) \]
Solution:
Using identity:
\[ (a-b)(a^2+ab+b^2)=a^3-b^3 \]
Here, \[ a=9y^2,\qquad b=4x^2 \]
\[ (9y^2 – 4x^2)(81y^4 + 36x^2y^2 + 16x^4) \]
\[ = (9y^2)^3-(4x^2)^3 \]
\[ = 729y^6-64x^6 \]
Substituting \[ x=3,\qquad y=-1 \]
\[ = 729(-1)^6-64(3)^6 \]
\[ = 729(1)-64(729) \]
\[ = 729-46656 \]
\[ =-45927 \]