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Missberberye
@Missberberye
April 2019
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Bonjour j'ai vraiment besoin d'aide c'est un devoir maison niveau 3e.
1. Développer et réduire les expressions ci-dessous (sauf K) en indiquant quelques étapes :
A= (3x + 2)²
B= (4x - 5)²
C= (3x - 4)² - (2x - 3)²
D= (2x + 1)² - (2x + 3)(2x - 2)
E= (4x + 3)(6x - 2) - (4x + 3)²
F= (2x + 5)² - (x + 1)²
G= (2x + 1)(x - 2) - (3x + 1)(2x + 1)
H= (1 - 3x)² - 3(1 - 3x)
I= (5x - 3)² - (2x - 5)²
J= (3x - 4)² - 49
K= 3x² + 2x
L= x - 3 + (x - 1)(x - 3)
2. Factoriser les expressions précédentes sauf A, B et D en indiquant quelques étapes.
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1. Développer et réduire les expressions ci-dessous (sauf K) en indiquant quelques étapes :
A= (3x + 2)² = 9x² +12x+4
B= (4x - 5)² = 16x² -40x+25
C= (3x - 4)² - (2x - 3)² = 9x²-24x+16 -(4x²-12x+9)
= 9x²-24x+16-4x²+12x-9 = 5x²-12x+7
D= (2x + 1)² - (2x + 3)(2x - 2) = 4x² +4x+1 -(4x²-4x+6x-6) =4x²+4x+1 -4x² -2x+6
= 2x +7
E= (4x + 3)(6x - 2) - (4x + 3)² = 24x²-8x+18x-6 -(16x²+24x+9)
= 24x² +10x-6 -16x²-24x-9 = 8x²-14x-15
F= (2x + 5)² - (x + 1)² = 4x²+20x+25 -(x²+2x+1) = 4x²+20x+25-x²-2x-1= 3x²+18x+24
G= (2x + 1)(x - 2) - (3x + 1)(2x + 1) = 2x²-4x+x-2 -(6x²+3x+2x+1) =2x²-3x-2-6x²-5x-1
= -4x²-8x-3
H= (1 - 3x)² - 3(1 - 3x) = 1 -6x+9x² -3+9x² = 18x² -6x -2
I= (5x - 3)² - (2x - 5)² = 25x²-30x+9 -(4x²-20x+25) =25x²-30x+9 -4x²+20x-25
= 21x² -10x-16
J= (3x - 4)² - 49 = 9x²-24x+16 -49 = 9x²-24x-33
K= 3x² + 2x
L= x - 3 + (x - 1)(x - 3) = x-3 +x²-3x-x+3 =x² -3x
2. Factoriser les expressions précédentes sauf A, B et D en indiquant quelques étapes.
A= (3x + 2)²
B= (4x - 5)²
C= (3x - 4)² - (2x - 3)² =(3x-4-2x+3)(2x-4+2x-3) =(x-1)(4x-7)
D= (2x + 1)² - (2x + 3)(2x - 2)
E= (4x + 3)(6x - 2) - (4x + 3)² = (4x+3)(6x-2-4x-3) =(4x+3)(2x-5)
F= (2x + 5)² - (x + 1)² =(2x+5-x-1)(2x+5+x+1) =(x+4)(3x+6) = 3(x+4)(x+2)
G= (2x + 1)(x - 2) - (3x + 1)(2x + 1) =(2x+1)(x-2-3x-1) =(2x+1)(-2x-3)
H= (1 - 3x)² - 3(1 - 3x) =(1-3x)(1-3x-3+9x) =(1-3x)(6x-2) = 2(1-3x)(3x-1)
I= (5x - 3)² - (2x - 5)² = (5x-3-2x+5)(5x-3+2x+5) =(3x+2)(7x+2)
J= (3x - 4)² - 49 = (3x - 4)² - 7² = (3x-4-7)(3x-4+7) =(3x-11)(3x+3) = 3(3x-11)(x+1)
K= 3x² + 2x = x((3x+2)
L= x - 3 + (x - 1)(x - 3) = (x-3) (1+x-1) =x(x-3)
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A= (3x + 2)² = 9x² +12x+4
B= (4x - 5)² = 16x² -40x+25
C= (3x - 4)² - (2x - 3)² = 9x²-24x+16 -(4x²-12x+9)
= 9x²-24x+16-4x²+12x-9 = 5x²-12x+7
D= (2x + 1)² - (2x + 3)(2x - 2) = 4x² +4x+1 -(4x²-4x+6x-6) =4x²+4x+1 -4x² -2x+6
= 2x +7
E= (4x + 3)(6x - 2) - (4x + 3)² = 24x²-8x+18x-6 -(16x²+24x+9)
= 24x² +10x-6 -16x²-24x-9 = 8x²-14x-15
F= (2x + 5)² - (x + 1)² = 4x²+20x+25 -(x²+2x+1) = 4x²+20x+25-x²-2x-1= 3x²+18x+24
G= (2x + 1)(x - 2) - (3x + 1)(2x + 1) = 2x²-4x+x-2 -(6x²+3x+2x+1) =2x²-3x-2-6x²-5x-1
= -4x²-8x-3
H= (1 - 3x)² - 3(1 - 3x) = 1 -6x+9x² -3+9x² = 18x² -6x -2
I= (5x - 3)² - (2x - 5)² = 25x²-30x+9 -(4x²-20x+25) =25x²-30x+9 -4x²+20x-25
= 21x² -10x-16
J= (3x - 4)² - 49 = 9x²-24x+16 -49 = 9x²-24x-33
K= 3x² + 2x
L= x - 3 + (x - 1)(x - 3) = x-3 +x²-3x-x+3 =x² -3x
2. Factoriser les expressions précédentes sauf A, B et D en indiquant quelques étapes.
A= (3x + 2)²
B= (4x - 5)²
C= (3x - 4)² - (2x - 3)² =(3x-4-2x+3)(2x-4+2x-3) =(x-1)(4x-7)
D= (2x + 1)² - (2x + 3)(2x - 2)
E= (4x + 3)(6x - 2) - (4x + 3)² = (4x+3)(6x-2-4x-3) =(4x+3)(2x-5)
F= (2x + 5)² - (x + 1)² =(2x+5-x-1)(2x+5+x+1) =(x+4)(3x+6) = 3(x+4)(x+2)
G= (2x + 1)(x - 2) - (3x + 1)(2x + 1) =(2x+1)(x-2-3x-1) =(2x+1)(-2x-3)
H= (1 - 3x)² - 3(1 - 3x) =(1-3x)(1-3x-3+9x) =(1-3x)(6x-2) = 2(1-3x)(3x-1)
I= (5x - 3)² - (2x - 5)² = (5x-3-2x+5)(5x-3+2x+5) =(3x+2)(7x+2)
J= (3x - 4)² - 49 = (3x - 4)² - 7² = (3x-4-7)(3x-4+7) =(3x-11)(3x+3) = 3(3x-11)(x+1)
K= 3x² + 2x = x((3x+2)
L= x - 3 + (x - 1)(x - 3) = (x-3) (1+x-1) =x(x-3)