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Identity (x+a)(x+b)

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

Expansion of $(2 a^{2} + 9) (2 a^{2} + 5)$ :
Using the identity $(x + a) (x + b) = x^{2} + (a + b) x + a b$
$(2 a^{2} + 9) \times (2 a^{2} + 5) = {(2 a^{2})}^{2} + (9 + 5) \times (2 a^{2}) + 9 \times 5 = 4 a^{4} + 14 \times (2 a^{2}) + 45 = 4 a^{4} + 28 a^{2} + 45$
Hence, $(2 a^{2} + 9) (2 a^{2} + 5) = 4 a^{4} + 28 a^{2} + 45$ .

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