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$(x + 3) (x + 5)$ can be expanded using which of the following identities?

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$(x + y) (x + y) = x^{2} + y^{2} + 2 x y$

$(x - y) (x - y) = x^{2} + y^{2} - 2 x y$

$(x + a) (x + b) = x^{2} + (a + b) x + a b$

$(x + y) (x - y) = x^{2} - y^{2}$

answer is C.

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Detailed Solution

$(x + a) (x + b) = x^{2} + (a + b) x + a b$ can be used to expand the product of $(x + 3) (x + 5)$ .

Using the identity:

$(x + 3) (x + 5) = x^{2} + (3 + 5) x + (5 \times 3)$

$\Rightarrow (x + 3) (x + 5) = x^{2} + 8 x + 15$

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