a(x) = x² - 9
= x² - 3²
= (x+3)(x-3)
b(x) = 4x² - 5
= (2x+√5)(2x-√5)
c(x) = 16x² - 49
= (4x+7)(4x-7)
d(x) = x² + 8x + 16
= (x+4)²
e(x) = 4x² -12x +9
= (2x+3)²
f(x) = 9-(2-x)²
= 3² - (2-x)²
= [3 + (2-x)][3 - (2-x)]
= (3 +2 -x)(3 -2 +x)
= (5 - x)(1 + x)
g(x) = (6x-1)² -4x²
= [(6x-1) + 2x][(6x-1) - 2x]
= (6x -1 +2x)(6x -1 -2x)
= (8x - 1)(4x -1)
h(x) = 49x² - (3x-4)²
= [7x + (3x-4)][7x - (3x-4)]
= (7x +3x -4)(7x -3x +4)
= (10x - 4)(4x + 4)
Voilà ;)
a) x²-9
x²-3²
(x-3)(x+3)
b) 4x²-5
(2x-racine de 5)(2x+racine de 5)
c) 16x²-49
(4x)²-7²
(4x-7)(4x+7)
d) x²+8x+16
x²+2fois xfois 4+4²
(x+4)²
e)4x²-12x+9
(2x)²-2fois2xfois3+3²
(2x-3)²
