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Show that ${(2x-1)}^{2}-{(x-3)}^{2}$ can be simplified to $(x+2)(3x-4)$.
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Using the principle of difference of two squares, we can factorize $(2x-1)^2-(x-3)^2$

Since $a^2-b^2 = (a+b)(a-b)$ so:

$(2x-1)^2-(x-3)^2$

$= [(2x-1) + (x-3)][(2x-1) - (x-3)]$

$=[2x+x-1-3][2x-1-x+3]$

$=[3x-4][x+2]$ which is the same as $(9x+2)(3x-4)$
by Diamond (40,709 points)

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