تحليل التعابير الجبرية

الحد الأول : 2x × (x + 1)

الحد الثاني : (2x - 2) × (x + 1)

2x(x + 1) + (2x - 2)(x + 1) = (x + 1)(2x + (2x - 2))

2x +(2x - 2) = 4x - 2

(5 - x)² = (5 - x) × (5 - x)

(5 - x)² = (−(x - 5)) × (5 - x) = −(x - 5)×(5 - x)

(x - 5)(x + 5) + (5 - x)²

= (x - 5)(x + 5) + (−(x - 5))×(5 - x)

= (x - 5)[(x + 5) - (5 - x)]

5x² − 15x = 5x(x − 3)

= 5x × (x - 3)

(x - 3)(4x - 1) + 5x² - 15x

= (x - 3)(4x - 1) + 5x × (x - 3)

= (x - 3)(4x - 1 + 5x)

(4 + 5)x = 9x

3x² − 6x = 3x(x − 2)

= 3x × (x - 2)

(x - 2)(x - 3) + 3x² - 6x

= (x - 2)(x - 3) + 3x × (x - 2)

= (x - 2)(x - 3 + 3x)

(1 + 3)x = 4x

20 = 4 × 5

4 = 4 × 1

العامل المشترك الأكبر = 4 (لأن pgcd(5,1) = 1)

20x + 4 = 4(5x + 1)

(6 - x)² = (6 - x) × (6 - x)

(6 - x)² = (−(x - 6)) × (6 - x) = −(x - 6)×(6 - x)

(x - 6)(2x + 2) + (6 - x)²

= (x - 6)(2x + 2) + (−(x - 6))×(6 - x)

= (x - 6)[(2x + 2) - (6 - x)]

الحد الأول : (x - 4) × (x - 1)

الحد الثاني : (x - 4) × (4x + 2)

(x - 4)(x - 1) + (x - 4)(4x + 2) = (x - 4)((x - 1) + (4x + 2))

معاملات x : 1 + 4 = 5

الثوابت : (-1) + (2) = 1

الحد الأول : (x - 8) × (6x - 5)

الحد الثاني : (x - 8) × (3x + 3)

(x - 8)(6x - 5) - (x - 8)(3x + 3) = (x - 8)((6x - 5) - (3x + 3))

معاملات x : 6 - 3 = 3

الثوابت : (-5) - (3) = -8

(6 - x)² = (6 - x) × (6 - x)

(6 - x)² = (−(x - 6)) × (6 - x) = −(x - 6)×(6 - x)

(x - 6)(2x - 3) - (6 - x)²

= (x - 6)(2x - 3) - (−(x - 6))×(6 - x)

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

الحد الأول : 2x × (3x + 2)

الحد الثاني : (x + 3) × (3x + 2)

2x(3x + 2) - (x + 3)(3x + 2) = (3x + 2)(2x - (x + 3))

2x -(x + 3) = x - 3