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factorize-x-1-2-4y-2-




Question Number 74163 by MASANJAJ last updated on 19/Nov/19
factorize  (x−1)^2  −4y^2
$${factorize} \\ $$$$\left({x}−\mathrm{1}\right)^{\mathrm{2}} \:−\mathrm{4}{y}^{\mathrm{2}} \\ $$
Answered by MJS last updated on 19/Nov/19
a^2 −b^2 =(a−b)(a+b)  (x−1)^2 −4y^2 =  =(x−1−2y)(x−1+2y)=  =(x−2y−1)(x+2y−1)
$${a}^{\mathrm{2}} −{b}^{\mathrm{2}} =\left({a}−{b}\right)\left({a}+{b}\right) \\ $$$$\left({x}−\mathrm{1}\right)^{\mathrm{2}} −\mathrm{4}{y}^{\mathrm{2}} = \\ $$$$=\left({x}−\mathrm{1}−\mathrm{2}{y}\right)\left({x}−\mathrm{1}+\mathrm{2}{y}\right)= \\ $$$$=\left({x}−\mathrm{2}{y}−\mathrm{1}\right)\left({x}+\mathrm{2}{y}−\mathrm{1}\right) \\ $$

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