waecmaths question:
Factorize: ${{(2x+3y)}^{2}}-{{(x-4y)}^{2}}$
Option A:
$(3x-y)(x+3y)$
Option B:
$(3x+y)(2x-7y)$
Option C:
$(3x+y)(x-7y)$
Option D:
$(3x-y)(2x+7y)$
waecmaths solution:
$\begin{align} & {{(2x+3y)}^{2}}-{{(x-4y)}^{2}} \\ & \text{Difference of two squares} \\ & =[2x+3y)-(x-4y)][(2x+3y)+(x-4y)] \\ & =[2x+3y-x+4y][2x+3y+x-4y] \\ & =(x+7y)(3x-y) \\ & =(3x-7)(x+7y) \\\end{align}$
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