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relenaden
@relenaden
August 2021
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Разложить на множители
x^2+2x-y^2+4y-3
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Cherfor
Дополняем до квадратов суммы и разности.
x^2+2x+1-1 = (x+1)^2-1
-(y^2-4y+4-4) = -(y-2)^2+4
(x+1)^2 - (y-2)^2 -1 + 4 - 3 = (x+1)^2 - (y-2)^2 = (x+1-y+2)(x+1+y-2) = (x-y+3)(x+y-1)
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Answers & Comments
x^2+2x+1-1 = (x+1)^2-1
-(y^2-4y+4-4) = -(y-2)^2+4
(x+1)^2 - (y-2)^2 -1 + 4 - 3 = (x+1)^2 - (y-2)^2 = (x+1-y+2)(x+1+y-2) = (x-y+3)(x+y-1)