نفكيك التعابير الجبرية

42 = 6 × 7

30 = 6 × 5

العامل المشترك الأكبر = 6 (لأن pgcd(7,5) = 1)

42x + 30 = 6(7x + 5)

(3 - x) = −(x - 3)

(x - 3)(3x + 3) + (3 - x)(5x - 3)

= (x - 3)(3x + 3) + (−(x - 3))(5x - 3)

= (x - 3)((3x + 3) − (5x - 3))

معاملات x : 3 − (1×5) = -2

الثوابت : 3 − (1×-3) = 6

(4 - x)² = (4 - x) × (4 - x)

(4 - x)² = (−(x - 4)) × (4 - x) = −(x - 4)×(4 - x)

(x - 4)(5x - 5) + (4 - x)²

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

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

(1 - x)² = (1 - x) × (1 - x)

(1 - x)² = (−(x - 1)) × (1 - x) = −(x - 1)×(1 - x)

(x - 1)(x - 3) + (1 - x)²

= (x - 1)(x - 3) + (−(x - 1))×(1 - x)

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

1x − 7 = 1(x − 7)

= 1 × (x - 7)

(x - 7)(5x + 1) + 1x - 7

= (x - 7)(5x + 1) + 1 × (x - 7)

= (x - 7)(5x + 1 + 1)

16 = 8 × 2

8 = 8 × 1

العامل المشترك الأكبر = 8 (لأن pgcd(2,1) = 1)

16x + 8 = 8(2x + 1)

4x² − 4x = 4x(x − 1)

= 4x × (x - 1)

(x - 1)(2x - 6) + 4x² - 4x

= (x - 1)(2x - 6) + 4x × (x - 1)

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

(2 + 4)x = 6x

الحد الأول : 5x × (3x + 5)

الحد الثاني : (x + 6) × (3x + 5)

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

5x -(x + 6) = 4x - 6

15 = 5 × 3

5 = 5 × 1

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

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

(4 - x) = −(x - 4)

(x - 4)(x + 3) + (4 - x)(4x - 6)

= (x - 4)(x + 3) + (−(x - 4))(4x - 6)

= (x - 4)((x + 3) − (4x - 6))

معاملات x : 1 − (1×4) = -3

الثوابت : 3 − (1×-6) = 9