نفكيك التعابير الجبرية

الحد الأول : (x - 6) × (2x + 6)

الحد الثاني : (x - 6) × (x - 5)

(x - 6)(2x + 6) + (x - 6)(x - 5) = (x - 6)((2x + 6) + (x - 5))

معاملات x : 2 + 1 = 3

الثوابت : (6) + (-5) = 1

(5 - x)² = (5 - x) × (5 - x)

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

(x - 5)(5x + 4) - (5 - x)²

= (x - 5)(5x + 4) - (−(x - 5))×(5 - x)

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

2x² − 2x = 2x(x − 1)

= 2x × (x - 1)

(x - 1)(4x - 6) + 2x² - 2x

= (x - 1)(4x - 6) + 2x × (x - 1)

= (x - 1)(4x - 6 + 2x)

(4 + 2)x = 6x

الحد الأول : (x - 5) × (6x - 2)

الحد الثاني : (x - 5) × (6x + 5)

(x - 5)(6x - 2) + (x - 5)(6x + 5) = (x - 5)((6x - 2) + (6x + 5))

معاملات x : 6 + 6 = 12

الثوابت : (-2) + (5) = 3

الحد الأول : (x - 7) × (2x + 5)

الحد الثاني : (x - 7) × (6x + 5)

(x - 7)(2x + 5) + (x - 7)(6x + 5) = (x - 7)((2x + 5) + (6x + 5))

معاملات x : 2 + 6 = 8

الثوابت : (5) + (5) = 10

2x² − 12x = 2x(x − 6)

= 2x × (x - 6)

(x - 6)(5x - 2) + 2x² - 12x

= (x - 6)(5x - 2) + 2x × (x - 6)

= (x - 6)(5x - 2 + 2x)

(5 + 2)x = 7x

5x − 20 = 5(x − 4)

= 5 × (x - 4)

(x - 4)(2x - 1) + 5x - 20

= (x - 4)(2x - 1) + 5 × (x - 4)

= (x - 4)(2x - 1 + 5)

الحد الأول : (x - 2) × (x + 3)

الحد الثاني : (x - 2) × (3x - 1)

(x - 2)(x + 3) + (x - 2)(3x - 1) = (x - 2)((x + 3) + (3x - 1))

معاملات x : 1 + 3 = 4

الثوابت : (3) + (-1) = 2

5x − 40 = 5(x − 8)

= 5 × (x - 8)

(x - 8)(4x - 5) + 5x - 40

= (x - 8)(4x - 5) + 5 × (x - 8)

= (x - 8)(4x - 5 + 5)

15 = 3 × 5

3 = 3 × 1

العامل المشترك الأكبر = 3 (لأن pgcd(5,1) = 1)

15x + 3 = 3(5x + 1)