waecmaths question:
Factorize completely the expression ${{(x+2)}^{2}}-{{(2x+1)}^{2}}$
Option A:
$(3x+2)(1-x)$
Option B:
$(3x+2)(2x+1)$
Option C:
$3{{(x+2)}^{2}}$
Option D:
$3(x+1)(1-x)$
waecmaths solution:
$\begin{align} & {{(x+2)}^{2}}-{{(2x+1)}^{2}}\left| {{a}^{2}}-{{b}^{2}}=(a-b)(a+b) \right. \\ & {{(x+2)}^{2}}-{{(2x+1)}^{2}}=[(x+2)+(2x+1)][(x+2)-(2x+1)] \\ & {{(x+2)}^{2}}-{{(2x+1)}^{2}}=(3x+3)(-x+1) \\ & {{(x+2)}^{2}}-{{(2x+1)}^{2}}=3(x+1)(1-x) \\\end{align}$
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