Explications étape par étape:
Développer :
a)
[tex](x + 7) {}^{2} = {x}^{2} + 2 \times x \times 7 + {7}^{2} \\ = {x}^{2} + 14x + 49[/tex]
b)
[tex](2x - 3) {}^{2} = (2x) {}^{2} - 2 \times 2x \times 3 + {3}^{2} \\ = {4x}^{2} - 12x + 9[/tex]
c)
[tex](x + 5)(x - 5) = {x}^{2} - 5 {}^{2} = x {}^{2} - 25[/tex]
d)
[tex](2x + 5)( x - 4) = 2x {}^{2} - 8x + 5x - 20 \\ = {2x}^{2} - 3x - 20[/tex]
factoriser :
e)
[tex] {4x}^{2} + 20x + 25 = {(2x)}^{2} + 2 \times 2x \times 5 + {5}^{2} \\ = (2x + 5) {}^{2} [/tex]
f)
[tex] {x}^{2} - 6x + 9 = {x}^{2} - 2 \times x \times 3 + {3}^{2} \\ = (x + 3) {}^{2} [/tex]
g)
[tex]81x {}^{2} - 49 = {(9x)}^{2} - 7 {}^{2} \\ = (9x - 7)(9x + 7) [/tex]
