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Algebraic Identity: (x + a)(x + b) = x^2 + (a + b)x + ab

Find the prod...

Question

Find the product of $(2 a^{2} + 9) (2 a^{2} + 5) .$

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Solution

Given: $(2 a^{2} + 9) (2 a^{2} + 5)$
This is in the form of $(x + a) (x + b)$ where $x = 2 a^{2}, a = 9 a n d b = 5.$

We know that,
$(x + a) (x + b) = x^{2} + (a + b) x + a b$
$(2 a^{2} + 9) (2 a^{2} + 5) = (2 a^{2})^{2} + (9 + 5) \times 2 a^{2} + 9 \times 5$
$= 4 a^{4} + 14 \times 2 a^{2} + 45$
$= 4 a^{4} + 28 a^{2} + 45$

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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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