Réponse:
Développement et réduction des expressions :
1. \( Z = (13x - 5)(2 + 3x) \)
\( Z = 13x(2) + 13x(3x) - 5(2) - 5(3x) \)
\( Z = 26x + 39x^2 - 10 - 15x \)
\( Z = 39x^2 + 11x - 10 \)
2. \( A = (8 + 6x)(7x - 4) \)
\( A = 8(7x) + 8(-4) + 6x(7x) + 6x(-4) \)
\( A = 56x - 32 + 42x^2 - 24x \)
\( A = 42x^2 + 32x - 32 \)
3. \( R = (-9 - 5x)(-10 - 2x) \)
\( R = -9(-10) - 9(-2x) - 5x(-10) - 5x(-2x) \)
\( R = 90 + 18x - 50x + 10x^2 \)
\( R = 10x^2 - 32x + 90 \)
Développement des expressions :
1. \( P = (7 + 4x)(7 - 4x) \)
\( P = 7(7) - 7(4x) + 4x(7) - 4x(4x) \)
\( P = 49 - 28x + 28x - 16x^2 \)
\( P = 49 - 16x^2 \)
2. \( I = (9x - 2)(9x + 2) \)
\( I = 9x(9x) + 9x(2) - 2(9x) - 2(2) \)
\( I = 81x^2 + 18x - 18x - 4 \)
\( I = 81x^2 - 4 \)
3. \( R = (-8x + 3)(-8x - 3) \)
\( R = -8x(-8x) - 8x(-3) + 3(-8x) + 3(3) \)
\( R = 64x^2 + 24x - 24x - 9 \)
\( R = 64x^2 - 9 \)
Factorisation des expressions :
1. \( C = 81 - 4x^2 \)
\( C = (9)^2 - (2x)^2 \)
\( C = (9 + 2x)(9 - 2x) \)
2. \( I = 16x^2 - 49 \)
\( I = (4x)^2 - (7)^2 \)
\( I = (4x + 7)(4x - 7) \)
3. \( G = 25 - 65x^2 \)
\( G = (5)^2 - (5x)^2 \)
\( G = (5 + 5x)(5 - 5x) \)
