Find the Product:
\[ (7p^4 + q)(49p^8 – 7p^4q + q^2) \]
Solution:
Using identity:
\[ (a+b)(a^2-ab+b^2)=a^3+b^3 \]
Here, \[ a=7p^4,\qquad b=q \]
\[ (7p^4 + q)(49p^8 – 7p^4q + q^2) \]
\[ = (7p^4 + q)\left[(7p^4)^2 – (7p^4)(q) + q^2\right] \]
\[ = (7p^4)^3 + q^3 \]
\[ = 343p^{12} + q^3 \]