Use suitable identities to find the following products:
$(2 x + 7) (3 x - 5)$

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Solution

We have, $(2 x + 7) (3 x + 5)$
$= 2 (x + \frac{7}{2}) . 3 (x - \frac{5}{3})$
$= 6 (x + \frac{7}{2}) (x - \frac{5}{3})$
$= 6 [x^{2} + (\frac{7}{2} - \frac{5}{3}) x + \frac{7}{2} \times \frac{- 5}{3}]$
$[∵ (x + a) (x + b) = x^{2} + (a + b) x + a b]$
$= 6 [x^{2} + (\frac{21 - 10}{6}) x - \frac{35}{6}]$
$= 6 x^{2} + 11 x - 35$

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