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Exercice 10 Développer et réduire
a A = (x + 4)(x - 6) + (-1 + x)(x - 7);
b B=(x - 1)(5.x - 2) -(-6 + 3.x)(-1 + x);
C=-(3x - 3)(x + 4) - (7x-8)(-1 + 7x);
d D= -(2x - 5)(3 - 4.x) +(6x - 9)-2x - 1).
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Bonsoir

Développer et réduire

a A = (x + 4)(x - 6) + (-1 + x)(x - 7)

A = x² - 6x + 4x - 24 - x + 7 + x² - 7x

A = x² + x² - 6x - 7x - x + 4x - 24 + 7

A = 2x² - 10x - 17

b B=(x - 1)(5.x - 2) -(-6 + 3.x)(-1 + x)

B = 5x² - 2x - 5x + 2 - (6 - 6x - 3x + 3x²)

B = 5x² - 2x - 5x + 2 - 6 + 6x + 3x - 3x²

B = 5x² - 3x² - 2x - 5x + 6x + 3x + 2 - 6

B = 2x² + 2x - 4

C=-(3x - 3)(x + 4) - (7x-8)(-1 + 7x)

C = - (3x² + 12x - 3x - 12) - (- 7x + 49x² + 8 - 56x)

C = - 3x² - 12x + 3x + 12 + 7x - 49x² - 8 + 56x

C = - 3x² - 49x² - 12x + 3x + 7x + 56x + 12 - 8

C = - 52x² + 54x + 4

d D= -(2x - 5)(3 - 4.x) +(6x - 9) (-2x - 1)

D = - (6x - 8x² - 15 + 20x) - 12x² - 6x + 18x + 9

D = - 6x + 8x² + 15 - 20x - 12x² - 6x + 18x + 9

D = - 12x² + 8x² - 6x - 6x + 18x - 20x  + 15 + 9

D = - 4x² - 14x + 24

Salut !

Développer et réduire.

A = ( x + 4 ) ( x - 6 ) + ( - 1 + x ) ( x - 7 )

A = x * x + x * ( - 6 ) + 4 * x + 4 * ( - 6 ) - 1 * x - 1 * ( - 7 ) + x * x + x * ( - 7 )

A = x² - 6x + 4x - 24 - x + 7 + x² - 7x

A = 2x² - 10x - 17 ✅

B = ( x - 1 ) ( 5x - 2 ) - ( - 6 + 3x ) ( - 1 + x )

B = x * 5x +x * ( - 2 ) - 1 * 5x - 1 * ( - 2 ) - ( - 6 * ( - 1 ) - 6 " x + 3x * ( - 1 ) + 3x * x )

B = 5x² - 2x - 5x + 2 - ( 6 - 6x - 3x + 3x² )

B = 5x² - 2x - 5x + 2 - 6 + 6x + 3x - 3x²

B = 2x² + 2x - 4 ✅

C = - ( 3x - 3 ) ( x + 4 ) - ( 7x - 8 ) ( - 1 + 7x )

C = - ( 3x * x + 3x * 4 - 3 * x - 3 * 4 ) - ( 7x * ( - 1 ) + 7x * 7x - 8 * ( - 1 ) - 8 * 7x )

C = - ( 3x² + 12x - 3x - 12 ) - ( - 7x + 49x² + 8 - 56x )

C = - 3x² - 12x + 3x + 12 + 7x - 49x² - 8 + 56x

C = - 52x² + 54x + 4 ✅

D = - ( 2x - 5 ) ( 3 - 4x ) + ( 6x - 9 ) ( - 2x - 1 )

D = - ( 2x * 3 + 2x * ( - 4x ) - 5 * 3 - 5 * ( - 4x ) + 6x * ( - 2x ) + 6x * ( - 1 ) - 9 * ( - 2x ) - 9 * ( - 1 )

D = - ( 6x - 8x² - 15 + 20x ) - 12x² - 6x + 18x + 9

D = - 6x + 8x² + 15 - 20x - 12x² - 6x + 18x + 9

D = - 4x² - 14x + 24 ✅

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