Factorise $(2x+3)^{2} - (x-1)^{2}$.

Factorise $(2x+3)^{2} - (x-1)^{2}$.
  1. $(3x+2)(x+4)$
  2. $(3x+2)(x-4)$
  3. $(3x-2)(x+4)$
  4. $(x+2)(3x+4)$

Solution

Use $a^{2}-b^{2}=(a-b)(a+b)$ with $a=2x+3, b=x-1$. $a-b = x+4$, $a+b = 3x+2$. So $(2x+3)^{2}-(x-1)^{2} = (x+4)(3x+2)$.

Asked in: IMO

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