Doprowadz do najprostszej postaci wyrażenia a następnie oblicz jego wartość liczbowa dla podanych wartości zmiennych zapisanych obok a) (x+2) do kwadratu-3(5-x) do kwadratu x=-2 b) 4(x-1) (x+1)-(2x-1) (2x+1) x=1/2 c) (x-y) do kwadratu- (x+y) do kwadrat

[latex]\a) \(x+2)^2-3(5-x)^2=x^2+4x+4-3(25-10x+x^2)= \ \x^2+4x+4-75+30x-3x^2=-2x^2+34x-71 \ \-2cdot(-2)^2+34cdot(-2)-71=-4-68-71=-143 \ \b) \4(x-1)(x+1)-(2x-1)(2x+1)=4(x^2-1)-(4x^2-1)= \ \4x^2-4-4x^2+1=-3 dla kazdego xinRe. [/latex] [latex]\c) \(x-y)^2-(x+y)^2=(x-y-x-y)(x-y+x+y)= \ \-2ycdot2x=-4xy \ \-4cdot0,5cdot(-0,2)=0,4 \ \d) \(3x-5y)(3x+5y)=9x^2-25y^2 \ \9cdot( frac{1}{9} )^2-25cdot(- frac{1}{5} )^2=9cdot dfrac{1}{9^2}-25cdotdfrac{1}{25} = \ \ dfrac{1}{9} -1=- dfrac{8}{9}[/latex]

[latex]a).(x+2) ^{2}-3(5-x) ^{2} = x^{2} +4x+4-3(25-10x+ x^{2} )= \ x^{2} +4x+4-75+30x-3 x^{2} =-2 x^{2} +34x-71 \ \ x=-2 \ -2*(-2) ^{2} +34*(-2)-71=-2*4-68-71=-8-68-71= \ =-76-71=-147 \ \ b).4(x-1)(x+1)-(2x-1)(2x+1)=4( x^{2} -1)-(4 x^{2} -1)= \ =4 x^{2} -4-4 x^{2} +1=-3 \ \ c).(x-y) x^{2} -(x+y) x^{2} = x^{2} -2xy+y ^{2} - x^{2} -2xy-y ^{2} =-4xy \ \ x=0,5,y=-0,2 \ -4*0,5*(-0,2)=-2*(-0,2)=0,4 [/latex] [latex]d).(3x-5y)(3x+5y)=(3x) ^{2} -(5y) ^{2} =9x ^{2} -25y ^{2} \ \ x= frac{1}{9} ,y=- frac{1}{5} \ \ 9*( frac{1}{9} ) ^{2} -25*(- frac{1}{5} ) ^{2} =9* frac{1}{81} -25* frac{1}{25} = frac{1}{9} -1= frac{1}{9}- frac{9}{9} =- frac{8}{9} [/latex]