Bonjour,
Exercice 1
1. D = [tex](5x-3)^{2} -(7x-2)(5x-3)[/tex] = [tex]((5x)^{2}-2*5x*3+3^{2})-(35x^{2} -21x-10x+6)[/tex] = [tex](25x^{2} -30x+9)-(35x^{2}-31x+6)[/tex] = [tex]25x^{2} -30x+9-35x^{2}+31x-6[/tex] = [tex]-10x^{2}+x+3[/tex]
2. D = [tex](5x-3)^{2} -(7x-2)(5x-3)[/tex] = [tex](5x-3)((5x-3)-(7x-2))[/tex] = [tex](5x-3)(5x-3-7x+2)[/tex] = [tex](5x-3)(-2x-1)[/tex]
3. Pour [tex]x=-2[/tex], D = [tex](5*(-2)-3)(-2*(-2)-1)[/tex] = [tex](-10-3)(4-1)[/tex] = [tex]-13*3[/tex] = [tex]-39[/tex]
4. Pour [tex]x=\frac{3}{5}[/tex], D = [tex]-10*(\frac{3}{5})^{2} +\frac{3}{5} +3[/tex] = [tex]-10*\frac{9}{25}+\frac{3}{5}+3[/tex] = [tex]-2*5*\frac{9}{5*5}+\frac{3}{5}+3[/tex] = [tex]-2*\frac{9}{5}+\frac{3}{5}+3[/tex] = [tex]\frac{-18}{5}+\frac{3}{5}+3[/tex] = [tex]\frac{-15}{5}+3[/tex] = [tex]-3+3[/tex] = [tex]0[/tex]
Exercice 2
1. A = [tex](6x-5)*(2+3x)-(5x+4)*(6x-5)[/tex] = [tex](6x-5)*((2+3x)-(5x+4))[/tex] = [tex](6x-5)(2+3x-5x-4)[/tex] = [tex](6x-5)*(-2-2x)[/tex] = [tex]-2(6x-5)(1+x)[/tex]
B = [tex]49x^{2} -112x+64[/tex] = [tex](7x)^2 -2*7x*8+8^{2}[/tex] = [tex](7x-8)^{2}[/tex]
C = [tex]x^{2}+\frac{8}{3}x+\frac{16}{9}[/tex] = [tex]\frac{1}{9}*(9x^{2} +24x+16)[/tex] = [tex]\frac{1}{9}*(3x+4)^{2}[/tex]
2. [tex](x^{2}+\frac{8}{3}x+\frac{16}{9})-25[/tex] = [tex](x+\frac{4}{3})^{2}-25[/tex] = [tex](x+\frac{4}{3})^{2}-5^{2}[/tex] = [tex](x+\frac{3}{4}-5)*(x+\frac{4}{3}+5)[/tex] = [tex](x-\frac{11}{3})*(x+\frac{19}{3})[/tex] = [tex]\frac{1}{3}*(3x-11)*\frac{1}{3}*(3x+19)[/tex] = [tex]\frac{1}{9}*(3x-11)*(3x+19)[/tex]
Voilà, n'hésite pas si tu as des questions ! Bonne journée et bonnes vacances ;-)
