Développer et réduire les expresions suivantes 1) a) f(x) =(x+1)²-4 b) g(x)=(x-3)(2x+1)-5 c) h(x) = (2x-3)² d) i(x)= x (x-3)² Factoriser à l'aide d'un facteur c

Bonjour,

Développer et réduire les expresions suivantes
1) a) f(x) =(x+1)²-4
f (x) = x² + 2x + 1 - 4
f (x) = x² + 2x - 3

b) g(x)=(x-3)(2x+1)-5
g (x) = 2x² + x - 6x - 3 - 5
g (x) = 2x² - 5x - 8

c) h(x) = (2x-3)²
h (x) = 4x² - 12x + 9

d) i(x)= x (x-3)²
i (x) = x (x² - 6x + 9)
i (x) = x³ - 6x² + 9x

Factoriser à l'aide d'un facteur commun :

a) j(x) = 7x+14
j (x) = 7 (x + 2)

b) k(x) = x(x-1)-2x
k (x) = x² - x - 2x
k (x) = x² - 3x
k (x) = x (x - 3)

c) l(x) = 2x(x+1)+x
i (x) = x (2x + 3)

d) m(x)=(x+1)(x+2)-(x+1)(2x-3) 
m (x) = (x + 1) [(x + 2) - (2x - 3)]
m (x) = (x + 1) (x + 2 - 2x + 3)
m (x) = (x + 1) (- x + 5)

1) a) f(x) =(x+1)²-4
1) a)
 f(x) =(x+1)²-4
=(x+1-2)(x+1+2)
=(x-1)(x+3)
=x²+3x-x-3
=x²+2x-3
b)
 g(x)=(x-3)(2x+1)-5
=2x²+x-6x-3-5
=2x²-5x-8
c)
h(x) = (2x-3)²
=4x²-12x+9
d)
 i(x)= x (x-3)²
=x(x²-6x+9)
=x³-6x²+9x

Factoriser à l'aide d'un facteur commun:
a) j(x) = 7x+14
=7(x+2)
b) k(x) = x(x-1)-2x
=x(x-1-2)
=x(x-3)

c) l(x) = 2x(x+1)+x
=x(2x+2+1)
d) m(x)=(x+1)(x+2)-(x+1)(2x-3)
=(x+1)((x+2)-(2x-3))
=(x+1)(x+2-2x+3)
=(x+1)(-x+5)