Question

Find the following product:  (p² + 16) \[\left( p^2 - \frac{1}{4} \right)\]

Answer 1

Here, we will use the identity​ \[\left( x + a \right)\left( x - b \right) = x^2 + \left( a - b \right)x - ab\].

\[\left( p^2 + 16 \right)\left( p^2 - \frac{1}{4} \right)\]

\[ = \left( p^2 \right)^2 + \left( 16 - \frac{1}{4} \right)\left( p^2 \right) - 16 \times \frac{1}{4}\]

\[ = p^4 + \frac{63}{4} p^2 - 4\]