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Question Number 42516 by Akashuac last updated on 27/Aug/18

(x−(1/2)a),(x−(5/2)a)=?  Solve Please.

$$\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{a}\right),\left(\mathrm{x}−\frac{\mathrm{5}}{\mathrm{2}}\mathrm{a}\right)=? \\ $$$$\mathrm{Solve}\:\mathrm{Please}. \\ $$

Commented by maxmathsup by imad last updated on 27/Aug/18

=(1/4)(2x−a)(2x−5a) =(1/4)(4x^2  −10ax −2ax +5a^2 )  =(1/4)(4x^2  −12ax +5a^2 ) =x^2  −3ax +(5/4) a^2  .

$$=\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{2}{x}−{a}\right)\left(\mathrm{2}{x}−\mathrm{5}{a}\right)\:=\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{4}{x}^{\mathrm{2}} \:−\mathrm{10}{ax}\:−\mathrm{2}{ax}\:+\mathrm{5}{a}^{\mathrm{2}} \right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{4}{x}^{\mathrm{2}} \:−\mathrm{12}{ax}\:+\mathrm{5}{a}^{\mathrm{2}} \right)\:={x}^{\mathrm{2}} \:−\mathrm{3}{ax}\:+\frac{\mathrm{5}}{\mathrm{4}}\:{a}^{\mathrm{2}} \:. \\ $$

Answered by Rio Michael last updated on 31/Aug/18

x^2 −((5xa)/2)−((xa)/2) + ((5a^2 )/4)  x^2  + ((5a^2 )/4) − ((6ax)/2)  ((4x^2  + 5a^2 −12ax)/4)

$${x}^{\mathrm{2}} −\frac{\mathrm{5}{xa}}{\mathrm{2}}−\frac{{xa}}{\mathrm{2}}\:+\:\frac{\mathrm{5}{a}^{\mathrm{2}} }{\mathrm{4}} \\ $$$${x}^{\mathrm{2}} \:+\:\frac{\mathrm{5}{a}^{\mathrm{2}} }{\mathrm{4}}\:−\:\frac{\mathrm{6}{ax}}{\mathrm{2}} \\ $$$$\frac{\mathrm{4}{x}^{\mathrm{2}} \:+\:\mathrm{5}{a}^{\mathrm{2}} −\mathrm{12}{ax}}{\mathrm{4}} \\ $$$$ \\ $$

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