تمارين الرياضيات مع الحلول التفصيلية

الحل التفصيلي

\[ \textbf{A} = 16a + 8b \]

\[ = 8 \cdot 2a + 8 \cdot b \]

\[ = 8(2a + b) \]

\[ \textbf{B} = -6a + 9b \]

\[ = 3 \cdot (-2a) + 3 \cdot 3b \]

\[ = 3(-2a + 3b) \]

\[ \textbf{C} = 18a - 2c \]

\[ = 2 \cdot 9a + 2 \cdot (-c) \]

\[ = 2(9a - c) \]

\[ \textbf{D} = -3a - 6x \]

\[ = -3 \cdot a + (-3) \cdot 2x \]

\[ = -3(a + 2x) \]

\[ \textbf{E} = 35 + 7xy \]

\[ = 7 \cdot 5 + 7 \cdot xy \]

\[ = 7(5 + xy) \]

\[ \textbf{F} = -22 - 3y \]

\[ = -1 \cdot 22 + (-1) \cdot 3y \]

\[ = -1(22 + 3y) \]

\[ \textbf{G} = -6x - 9y \]

\[ = -3 \cdot 2x + (-3) \cdot 3y \]

\[ = -3(2x + 3y) \]

\[ \textbf{H} = -12x - 6y - 18 \]

\[ = -6 \cdot 2x + (-6) \cdot y + (-6) \cdot 3 \]

\[ = -6(2x + y + 3) \]

\[ \textbf{I} = 12xy - 24xyz + 36xyt \]

\[ = 12xy \cdot 1 + 12xy \cdot (-2z) + 12xy \cdot 3t \]

\[ = 12xy(1 - 2z + 3t) \]

\[ \textbf{J} = 20xyz - 4xy + 12xy \]

\[ = 4xy \cdot 5z + 4xy \cdot (-1) + 4xy \cdot 3 \]

\[ = 4xy(5z - 1 + 3) \]

\[ = 4xy(5z + 2) \]

الحل التفصيلي

\[ \textbf{A} = 3a + a(b + 3) \]

\[ = a \cdot 3 + a \cdot (b + 3) \]

\[ = a(3 + b + 3) \]

\[ = a(b + 6) \]

\[ \textbf{B} = 5a - 7a(b - 4) \]

\[ = a \cdot 5 - a \cdot 7(b - 4) \]

\[ = a[5 - 7(b - 4)] \]

\[ = a[5 - 7b + 28] \]

\[ = a(33 - 7b) \]

\[ \textbf{C} = 13a(x - y) - a \]

\[ = a \cdot 13(x - y) - a \cdot 1 \]

\[ = a[13(x - y) - 1] \]

\[ = a(13x - 13y - 1) \]

\[ \textbf{D} = a - 3a(x + y) \]

\[ = a \cdot 1 - a \cdot 3(x + y) \]

\[ = a[1 - 3(x + y)] \]

\[ = a(1 - 3x - 3y) \]

\[ \textbf{E} = 5(x + 4) + 4(x + 4) \]

\[ = (5 + 4)(x + 4) \]

\[ = 9(x + 4) \]

\[ \textbf{F} = (x - 3) - 8(x - 3) \]

\[ = 1 \cdot (x - 3) - 8 \cdot (x - 3) \]

\[ = (1 - 8)(x - 3) \]

\[ = -7(x - 3) \]

\[ \textbf{G} = 7(5 - x) + a(5 - x) \]

\[ = (7 + a)(5 - x) \]

\[ \textbf{H} = 3x(x - 4) - (x - 4)x \]

\[ = (x - 4) \cdot 3x - (x - 4) \cdot x \]

\[ = (x - 4)(3x - x) \]

\[ = (x - 4)(2x) \]

الحل التفصيلي

\[ \textbf{A} = 5a(2x - 3) - b(3 - 2x) \]

\[ = 5a(2x - 3) + b(2x - 3) \]

\[ = (5a + b)(2x - 3) \]

\[ \textbf{B} = 6b(2a + 5) - 5(-2a - 5) \]

\[ = 6b(2a + 5) + 5(2a + 5) \]

\[ = (6b + 5)(2a + 5) \]

\[ \textbf{C} = 3c(6x - 7) + 2b(7 - 6x) \]

\[ = 3c(6x - 7) - 2b(6x - 7) \]

\[ = (3c - 2b)(6x - 7) \]

\[ \textbf{D} = 3(5x + 6) - b(-6 - 5x) \]

\[ = 3(5x + 6) + b(5x + 6) \]

\[ = (3 + b)(5x + 6) \]

\[ \textbf{E} = 5x(3x - 4) - 3x + 4 \]

\[ = 5x(3x - 4) - (3x - 4) \]

\[ = (5x - 1)(3x - 4) \]

\[ \textbf{F} = 6(4x - 11) - 4x + 11 \]

\[ = 6(4x - 11) - (4x - 11) \]

\[ = (6 - 1)(4x - 11) \]

\[ = 5(4x - 11) \]

\[ \textbf{G} = 5x + 15 - 2a(x + 3) \]

\[ = 5(x + 3) - 2a(x + 3) \]

\[ = (5 - 2a)(x + 3) \]

\[ \textbf{H} = 6x + 9 - 7(2x + 3) \]

\[ = 3(2x + 3) - 7(2x + 3) \]

\[ = (3 - 7)(2x + 3) \]

\[ = -4(2x + 3) \]

\[ \textbf{I} = 8(x + 3) + 18 - 6x \]

\[ = 8x + 24 + 18 - 6x \]

\[ = (8x - 6x) + (24 + 18) \]

\[ = 2x + 42 \]

\[ = 2(x + 21) \]

الحل التفصيلي

\[ \textbf{A} = (x - 2y)(3x - 4) - 12x + 24y \]

\[ = (x - 2y)(3x - 4) - 12(x - 2y) \]

\[ = (x - 2y)(3x - 4 - 12) \]

\[ = (x - 2y)(3x - 16) \]

\[ \textbf{B} = (3x - 1)y - 5(6x - 2) \]

\[ = y(3x - 1) - 5 \cdot 2(3x - 1) \]

\[ = (y - 10)(3x - 1) \]

\[ \textbf{C} = (2x - 7)(5 - y) - 7(25 - 5y) \]

\[ = (2x - 7)(5 - y) - 7 \cdot 5(5 - y) \]

\[ = (2x - 7 - 35)(5 - y) \]

\[ = (2x - 42)(5 - y) \]

\[ = 2(x - 21)(5 - y) \]

\[ \textbf{D} = (2x - 5) - (6x - 15)(3x + 12) \]

\[ = (2x - 5) - 3(2x - 5)(3x + 12) \]

\[ = (2x - 5)[1 - 3(3x + 12)] \]

\[ = (2x - 5)(1 - 9x - 36) \]

\[ = (2x - 5)(-9x - 35) \]

\[ \textbf{E} = (2x - 5)(3x + 4) - (2x - 5)(x + 6) \]

\[ = (2x - 5)[(3x + 4) - (x + 6)] \]

\[ = (2x - 5)(3x + 4 - x - 6) \]

\[ = (2x - 5)(2x - 2) \]

\[ = 2(2x - 5)(x - 1) \]

\[ \textbf{F} = (3 + 7x)(1 - 3x) - (7x + 3)(2x - 5) \]

\[ = (7x + 3)(1 - 3x) - (7x + 3)(2x - 5) \]

\[ = (7x + 3)[(1 - 3x) - (2x - 5)] \]

\[ = (7x + 3)(1 - 3x - 2x + 5) \]

\[ = (7x + 3)(6 - 5x) \]

\[ \textbf{G} = 2(4 - 5x)(5 - 2x) - 5(4 - 5x)(7x + 1) \]

\[ = (4 - 5x)[2(5 - 2x) - 5(7x + 1)] \]

\[ = (4 - 5x)[(10 - 4x) - (35x + 5)] \]

\[ = (4 - 5x)(10 - 4x - 35x - 5) \]

\[ = (4 - 5x)(5 - 39x) \]

\[ \textbf{H} = 7(1 - 3x)(4 - 3x) + 2(7x - 4)(1 - 3x) \]

\[ = (1 - 3x)[7(4 - 3x) + 2(7x - 4)] \]

\[ = (1 - 3x)[(28 - 21x) + (14x - 8)] \]

\[ = (1 - 3x)(28 - 21x + 14x - 8) \]

\[ = (1 - 3x)(20 - 7x) \]

\[ \textbf{I} = 4(2 - x)(4x + 7) - (x - 2)(1 - 3x) \]

\[ = 4(2 - x)(4x + 7) + (2 - x)(1 - 3x) \]

\[ = (2 - x)[4(4x + 7) + (1 - 3x)] \]

\[ = (2 - x)(16x + 28 + 1 - 3x) \]

\[ = (2 - x)(13x + 29) \]

\[ \textbf{J} = 7(x - 1)(2x + 3) + (1 - x)(6x - 5) \]

\[ = 7(x - 1)(2x + 3) - (x - 1)(6x - 5) \]

\[ = (x - 1)[7(2x + 3) - (6x - 5)] \]

\[ = (x - 1)(14x + 21 - 6x + 5) \]

\[ = (x - 1)(8x + 26) \]

\[ = 2(x - 1)(4x + 13) \]