Question

Find the following product:  (x² + 4) (x² + 9)

Answer 1

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

\[\left( x^2 + 4 \right)\left( x^2 + 9 \right)\]

\[ = \left( x^2 \right)^2 + \left( 4 + 9 \right)\left( x^2 \right) + 4 \times 9\]

\[ = x^4 + 13 x^2 + 36\]