Question:
If \[ x=-2 \quad \text{and} \quad y=1 \] find the value of:
\[ (4y^2 – 9x^2)(16y^4 + 36x^2y^2 + 81x^4) \]
Solution:
Using identity:
\[ (a-b)(a^2+ab+b^2)=a^3-b^3 \]
Here, \[ a=4y^2,\qquad b=9x^2 \]
\[ (4y^2 – 9x^2)(16y^4 + 36x^2y^2 + 81x^4) \]
\[ = (4y^2)^3-(9x^2)^3 \]
\[ = 64y^6-729x^6 \]
Substituting \[ x=-2,\qquad y=1 \]
\[ = 64(1)^6-729(-2)^6 \]
\[ = 64-729(64) \]
\[ = 64-46656 \]
\[ =-46592 \]