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Algebraic Identities

Use the ident...

Question

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

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Solution

$(2 a^{2} + 9) (2 a^{2} + 5)$
$= (2 a^{2})^{2} + (9 + 5) (2 a^{2}) + (9 \times 5)$
$= 4 a^{4} + 28 a^{2} + 45$

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