Réponse :
Explications étape par étape
bjr,
( x + 1)(2x + 1) =
double distributivité :
x*2x = 2x²
x*1 = x
1*2x = 2x
1*1 = 1
=>
2x² +x +2x+1 = 2x² +3x +1
b. ( 3x + 1)(2x + 2) = 6x² +6x + 2x+ 2 = 6x² + 8x +2
c. ( 2x + 1)(5 − 2x ) = 10x -4x² +5 -2x = -4x² +8x +5
d. ( 3x − 2 )(1 − x ) = 6x -3x² -2 +x = -3x² +7x -2
e. − ( x + 1)(2x − 3 ) = (-x-1)(2x-3) = -2x² +3x -2x +3 = -2x² -x +3
attention au signe négatif devant les parenthèses
f. 2 ( 1 − x )(2 − x ) =
simple distributivité et double distributivité
2*1 = 2
2*-x =-2x
(2-2x) ( 2-x) = 4 -2x -4x +2x² = 2x² -6x +4
☺
Bonjour,
a) (x+1)(2x+1)
= x*2x+x*1+1*2x+1*1
= 2x²+x+2x+1
= 2x²+3x+1
b) (3x+1)(2x+2)
= 3x*2x+3x*2+1*2x+1*2
= 6x²+6x+2x+2
= 6x²+8x+2
c) (2x+1)(5-2x)
= 2x*5-2x*2x+1*5-1*2x
= 10x-4x²+5-2x
= 8x-4x²+5
d) (3x-2)(1-x)
= 3x*1-3x*x-2*1-2*-x
= 3x-3x²-2+2x
= 5x-3x²-2
e) -(x+1)(2x-3)
=-(x*2x-x*3+1*2x-1*3)
=-(2x²-3x+2x-3)
=-(2x²-x-3)
=-2x²+x+3
f) 2(1-x)(2-x)
=2(1*2-1*x-x*2-x*-x)
=2(2-x-2x+x²)
=2(2-3x+x²)
= 2*2-2*3x+2*x²
= 4-6x+2x²
Bonne journée !