Use the identity $(x + a) (x + b) = x^{2} + (a + b) x + a b$ to find the product of $({2 a}^{2} + 9) ({2 a}^{2} + 5)$ .

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Solution

Using the identity,
$(x + a) (x + b) = x^{2} + (a + b) x + a b$
To find the product of $({2 a}^{2} + 9) ({2 a}^{2} + 5)$
we have, $x = 2 a^{2}$ , $a = 9$ and $b = 5$

$∴ (2 a^{2} + 9) (2 a^{2} + 5)$
$= {(2 a^{2})}^{2} + (9 + 5) 2 a^{2} + (9) (5)$
$= 4 a^{4} + 28 a^{2} + 45$
Therefore, the required product is $4 a^{4} + 28 a^{2} + 45$ .

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