Question

Find the following product: \[\left( z + \frac{3}{4} \right)\left( z + \frac{4}{3} \right)\]

Answer 1

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

\[\left( z + \frac{3}{4} \right)\left( z + \frac{4}{3} \right)\]

\[ = z^2 + \left( \frac{3}{4} + \frac{4}{3} \right)x + \frac{3}{4} \times \frac{4}{3}\]

\[ = z^2 + \frac{25}{12}z + 1\]