قم بتوزيع العبارات التالية:
\[ A = 3a(b + d) \]
\[ B = 2a(-6 - b + d) \]
\[ C = 3b(2a - 7c + 5d) \]
\[ D = a(2b - 3d + 5c) \]
\[ E = 4c(-2a - 3b - 5d) \]
\[ F = 5a(2c - 6b + 3d) \]
\[ G = -4a(-b + 2c - 8b) \]
\[ H = -2a(-6b - 2c + 5d) \]
\[ \textbf{A} = 3a(b + d) \]
\[ = 3a \cdot b + 3a \cdot d \]
\[ = 3ab + 3ad \]
\[ \textbf{B} = 2a(-6 - b + d) \]
\[ = 2a \cdot (-6) + 2a \cdot (-b) + 2a \cdot d \]
\[ = -12a - 2ab + 2ad \]
\[ \textbf{C} = 3b(2a - 7c + 5d) \]
\[ = 3b \cdot 2a + 3b \cdot (-7c) + 3b \cdot 5d \]
\[ = 6ab - 21bc + 15bd \]
\[ \textbf{D} = a(2b - 3d + 5c) \]
\[ = a \cdot 2b + a \cdot (-3d) + a \cdot 5c \]
\[ = 2ab - 3ad + 5ac \]
\[ \textbf{E} = 4c(-2a - 3b - 5d) \]
\[ = 4c \cdot (-2a) + 4c \cdot (-3b) + 4c \cdot (-5d) \]
\[ = -8ac - 12bc - 20cd \]
\[ \textbf{F} = 5a(2c - 6b + 3d) \]
\[ = 5a \cdot 2c + 5a \cdot (-6b) + 5a \cdot 3d \]
\[ = 10ac - 30ab + 15ad \]
\[ \textbf{G} = -4a(-b + 2c - 8b) \]
\[ = -4a \cdot (-b) + (-4a) \cdot 2c + (-4a) \cdot (-8b) \]
\[ = 4ab - 8ac + 32ab \]
\[ = (4ab + 32ab) - 8ac \]
\[ = 36ab - 8ac \]
\[ \textbf{H} = -2a(-6b - 2c + 5d) \]
\[ = -2a \cdot (-6b) + (-2a) \cdot (-2c) + (-2a) \cdot 5d \]
\[ = 12ab + 4ac - 10ad \]
قم بتوزيع العبارات التالية:
\[ A = (3 + a)(4 + b) \]
\[ B = (-3 + 2a)(5 - 3b) \]
\[ C = (-2a - 5)(2b - 3) \]
\[ D = (3a - 2b - 7)(2 - 5c) \]
\[ E = (2a - 3)(-2b + 3c - 5) \]
\[ F = (-2a - 5b + 8)(-3c - 9) \]
\[ \textbf{A} = (3 + a)(4 + b) \]
\[ = 3 \cdot 4 + 3 \cdot b + a \cdot 4 + a \cdot b \]
\[ = 12 + 3b + 4a + ab \]
\[ \textbf{B} = (-3 + 2a)(5 - 3b) \]
\[ = (-3) \cdot 5 + (-3) \cdot (-3b) + 2a \cdot 5 + 2a \cdot (-3b) \]
\[ = -15 + 9b + 10a - 6ab \]
\[ \textbf{C} = (-2a - 5)(2b - 3) \]
\[ = (-2a) \cdot 2b + (-2a) \cdot (-3) + (-5) \cdot 2b + (-5) \cdot (-3) \]
\[ = -4ab + 6a - 10b + 15 \]
\[ \textbf{D} = (3a - 2b - 7)(2 - 5c) \]
\[ = 3a \cdot 2 + 3a \cdot (-5c) + (-2b) \cdot 2 + (-2b) \cdot (-5c) + (-7) \cdot 2 + (-7) \cdot (-5c) \]
\[ = 6a - 15ac - 4b + 10bc - 14 + 35c \]
\[ \textbf{E} = (2a - 3)(-2b + 3c - 5) \]
\[ = 2a \cdot (-2b) + 2a \cdot 3c + 2a \cdot (-5) + (-3) \cdot (-2b) + (-3) \cdot 3c + (-3) \cdot (-5) \]
\[ = -4ab + 6ac - 10a + 6b - 9c + 15 \]
\[ \textbf{F} = (-2a - 5b + 8)(-3c - 9) \]
\[ = (-2a) \cdot (-3c) + (-2a) \cdot (-9) + (-5b) \cdot (-3c) + (-5b) \cdot (-9) + 8 \cdot (-3c) + 8 \cdot (-9) \]
\[ = 6ac + 18a + 15bc + 45b - 24c - 72 \]
قم بتوزيع العبارات التالية:
\[ A = a(2 - b) - 2b(3 + a) \]
\[ B = 7ab - 2a(-5 - b) + 3a(-3b - 9) \]
\[ C = 2a(-3b - 5) - 4(3a - 6b) \]
\[ D = 7(a - 1) + (2a - 5)(b - 3) \]
\[ E = (3a - 2)(b - 3) - (5a - 2)(b - 3) \]
\[ F = (6b - 3)(2a - 5) - 3a(2b - 7) \]
\[ \textbf{A} = a(2 - b) - 2b(3 + a) \]
\[ = a \cdot 2 - a \cdot b - (2b \cdot 3 + 2b \cdot a) \]
\[ = 2a - ab - 6b - 2ab \]
\[ = 2a - (ab + 2ab) - 6b \]
\[ = 2a - 3ab - 6b \]
\[ \textbf{B} = 7ab - 2a(-5 - b) + 3a(-3b - 9) \]
\[ = 7ab - [2a \cdot (-5) + 2a \cdot (-b)] + [3a \cdot (-3b) + 3a \cdot (-9)] \]
\[ = 7ab - (-10a - 2ab) + (-9ab - 27a) \]
\[ = 7ab + 10a + 2ab - 9ab - 27a \]
\[ = (7ab + 2ab - 9ab) + (10a - 27a) \]
\[ = 0ab - 17a \]
\[ = -17a \]
\[ \textbf{C} = 2a(-3b - 5) - 4(3a - 6b) \]
\[ = [2a \cdot (-3b) + 2a \cdot (-5)] - [4 \cdot 3a - 4 \cdot 6b] \]
\[ = -6ab - 10a - (12a - 24b) \]
\[ = -6ab - 10a - 12a + 24b \]
\[ = -6ab + (-10a - 12a) + 24b \]
\[ = -6ab - 22a + 24b \]
\[ \textbf{D} = 7(a - 1) + (2a - 5)(b - 3) \]
\[ = 7a - 7 + [2a \cdot b + 2a \cdot (-3) + (-5) \cdot b + (-5) \cdot (-3)] \]
\[ = 7a - 7 + (2ab - 6a - 5b + 15) \]
\[ = 7a - 7 + 2ab - 6a - 5b + 15 \]
\[ = (7a - 6a) + 2ab - 5b + (-7 + 15) \]
\[ = a + 2ab - 5b + 8 \]
\[ \textbf{E} = (3a - 2)(b - 3) - (5a - 2)(b - 3) \]
\[ = [3a \cdot b + 3a \cdot (-3) + (-2) \cdot b + (-2) \cdot (-3)] - [5a \cdot b + 5a \cdot (-3) + (-2) \cdot b + (-2) \cdot (-3)] \]
\[ = (3ab - 9a - 2b + 6) - (5ab - 15a - 2b + 6) \]
\[ = 3ab - 9a - 2b + 6 - 5ab + 15a + 2b - 6 \]
\[ = (3ab - 5ab) + (-9a + 15a) + (-2b + 2b) + (6 - 6) \]
\[ = -2ab + 6a + 0b + 0 \]
\[ = -2ab + 6a \]
\[ \textbf{F} = (6b - 3)(2a - 5) - 3a(2b - 7) \]
\[ = [6b \cdot 2a + 6b \cdot (-5) + (-3) \cdot 2a + (-3) \cdot (-5)] - [3a \cdot 2b + 3a \cdot (-7)] \]
\[ = (12ab - 30b - 6a + 15) - (6ab - 21a) \]
\[ = 12ab - 30b - 6a + 15 - 6ab + 21a \]
\[ = (12ab - 6ab) + (-6a + 21a) - 30b + 15 \]
\[ = 6ab + 15a - 30b + 15 \]
قم بتوزيع العبارات التالية:
\[ A = 5(3 - 2x) - 7(2x + 3) + 4(2x + 3) \]
\[ B = 8x - 11(3x + 7) - 2[6x + 1 - 3(2x - 1)] \]
\[ C = 2[3 + 2(3x + 1)] - 5[-2y(1 - x) + (4x - 1)(5y + 3)] \]
\[ \textbf{A} = 5(3 - 2x) - 7(2x + 3) + 4(2x + 3) \]
\[ = 5 \cdot 3 + 5 \cdot (-2x) - [7 \cdot 2x + 7 \cdot 3] + [4 \cdot 2x + 4 \cdot 3] \]
\[ = 15 - 10x - (14x + 21) + (8x + 12) \]
\[ = 15 - 10x - 14x - 21 + 8x + 12 \]
\[ = (-10x - 14x + 8x) + (15 - 21 + 12) \]
\[ = -16x + 6 \]
\[ \textbf{B} = 8x - 11(3x + 7) - 2[6x + 1 - 3(2x - 1)] \]
\[ = 8x - [11 \cdot 3x + 11 \cdot 7] - 2[6x + 1 - (3 \cdot 2x + 3 \cdot (-1))] \]
\[ = 8x - (33x + 77) - 2[6x + 1 - (6x - 3)] \]
\[ = 8x - 33x - 77 - 2[6x + 1 - 6x + 3] \]
\[ = 8x - 33x - 77 - 2[4] \]
\[ = 8x - 33x - 77 - 8 \]
\[ = (8x - 33x) - 77 - 8 \]
\[ = -25x - 85 \]
\[ \textbf{C} = 2[3 + 2(3x + 1)] - 5[-2y(1 - x) + (4x - 1)(5y + 3)] \]
\[ = 2[3 + 2 \cdot 3x + 2 \cdot 1] - 5[(-2y \cdot 1 + (-2y) \cdot (-x)) + (4x \cdot 5y + 4x \cdot 3 + (-1) \cdot 5y + (-1) \cdot 3)] \]
\[ = 2[3 + 6x + 2] - 5[(-2y + 2xy) + (20xy + 12x - 5y - 3)] \]
\[ = 2[5 + 6x] - 5[-2y + 2xy + 20xy + 12x - 5y - 3] \]
\[ = 2 \cdot 5 + 2 \cdot 6x - 5[12x + (2xy + 20xy) - 2y - 5y - 3] \]
\[ = 10 + 12x - 5[12x + 22xy - 7y - 3] \]
\[ = 10 + 12x - [5 \cdot 12x + 5 \cdot 22xy + 5 \cdot (-7y) + 5 \cdot (-3)] \]
\[ = 10 + 12x - (60x + 110xy - 35y - 15) \]
\[ = 10 + 12x - 60x - 110xy + 35y + 15 \]
\[ = (12x - 60x) + (-110xy) + (35y) + (10 + 15) \]
\[ = -48x - 110xy + 35y + 25 \]