Use the identity $(x + a) (x + b) = x^{2} + (a + b) x + a b$ to find the following product:
(i) $(2 x + 5 y) (2 x + 3 y)$ (ii) $(2 a^{2} + 9) (2 a^{2} + 5)$

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Solution

(i)
$(2 x + 5 y) (2 x + 3 y)$
$(2 x)^{2} + 2 x (5 y + 3 y) + (5 y) (3 y)$
$4 x^{2} + 16 x y + 15 y^{2}$
(ii)
$(2 a^{2} + 9) (2 a^{2} + 5)$
$(2 a)^{2} + 2 a^{2} (9 + 5) + (9) (5)$
$4 a^{4} + 28 a^{2} + 45$

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