2. Utilizați formulele de calcul prescurtat în exercițiile următoare:
[tex]a)\:(x+2)^2+(x-3)^2-(x+1)(x-1)=\\[/tex]
[tex]=x^2+4x+4+x^2-6x+9-x^2+1=\\[/tex]
[tex]=\bf x^2-2x+14\\[/tex]
[tex]b)\:(2x+1)^2-(x+6)(x-6)-3(x-2)^2=\\[/tex]
[tex]=4x^2+4x+1-x^2+36-3x^2+12x-12=\\[/tex]
[tex]=\bf 16x+25\\[/tex]
[tex]c)\:(x-5)^2-(x-4)(x+4)+(x+1)^2=\\[/tex]
[tex]=x^2-10x+25-x^2+16+x^2+2x+1=\\[/tex]
[tex]=\bf x^2-8x+42\\[/tex]
[tex]d)\:(3x-2)^2-5(x-3)(x+3)-(2x+3)^2=\\[/tex]
[tex]=9x^2-12x+4-5x^2+45-4x^2-12x-9=\\[/tex]
[tex]=\bf-24x+40\\[/tex]
[tex]e)\:(6x-5)^2-(5x + 4)(5x-4)-(4x + 3)^2=\\[/tex]
[tex]=36x^2-60x+25-25x^2+16-16x^2-24x-9=\\[/tex]
[tex]=\bf -5x^2-84x+32\\[/tex]
[tex]f)\:(5x-2)^2-(3x-4)(3x+4)-(4x+1)^2=\\[/tex]
[tex]=25x^2-20x+4-9x^2+16-16x^2-8x-1=\\[/tex]
[tex]=\bf-28x+19\\[/tex]
[tex]g)\:(4x-3y)^2-(2x+5y)(2x-5y)-(3x+y)(3x-y)=\\[/tex]
[tex]=16x^2-24xy+9y^2-4x^2+25y^2-9x^2+y^2=\\[/tex]
[tex]=\bf3x^2-24xy+35y^2\\[/tex]
[tex]h)\:(3x+y)^2-(2x-5y)^2-(x-2y)(x+2y)=\\[/tex]
[tex]=9x^2+6xy+y^2-4x^2+20xy-25y^2-x^2+4y^2=\\[/tex]
[tex]=\bf4x^2+26xy-20y^2\\[/tex]
_________________
Pentru rezolvarea acestui exercițiu am folosit următoarele formule de calcul prescurtat:
[tex]\bf\red{\boxed{ (x+y)^2=x^2+2xy+y^2 }}\\[/tex]
[tex]\bf\purple{\boxed{ (x-y)^2=x^2-2xy+y^2 }}\\[/tex]
[tex]\bf\blue{\boxed{ (x+y)(x-y)=x^2-y^2 }}\\[/tex]
Succes! ❀
Echipa BrainlyRO
