Find the product $(2x + 3)(2x + 5)$ using identity.

Find the product $(2x + 3)(2x + 5)$ using identity.
  1. $4x^{2} + 16x + 15$
  2. $4x^{2} + 8x + 15$
  3. $4x^{2} + 16x + 8$
  4. $2x^{2} + 16x + 15$

Solution

Let $X = 2x$: $(X+3)(X+5) = X^{2} + 8X + 15 = 4x^{2} + 16x + 15$.

Asked in: IMO

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