SUMA POR SU DIFERENCIA
Es igual a la diferencia de los cuadrados de los términos, es decir.
(a + b) (a - b) = a ² - b ²
Ejercicios resueltos
1. (u - v)(u + v) = u² - v²
- 2. (x + 2y)(x - 2y) = (x)² – (2y)² = x² – 4y²
3. (3a - b)(3a + b) = (3a)² - (b)² = 9a² - b²
4. (5x² - 3y)(5x² + 3y)= (5x²)² – (3y)² =25x⁴ - 9y²
5. (2x - 3xy)(2x + 3xy)=(2x)²–(3xy)²= 4x²- 9x²y²
6. (6a + 1)( 6a – 1) = (6a)² - (1)² = 36a ² - 1
7. (9m²-3n)(9m² +3n)= (9m²)² – (3n)²= 81a⁴ - 9n ²
8. (- 4a²b + 5b)(4a²b + 5b) = (5b - 4a²b)( 5b + 4a²b) = (5b)² – (4a²b)² = 25b ² - 16a4b²
9. (- 6m² n³ - 7m)(- 6m² n³ + 7m) = (- 6m²n³)² - (7m) ² = 36m⁴n6 - 49m²
10. (10a² – 1)(10a² + 1) = (10x²)² - (- 1)² =
= 100x⁴ - 1
11. (b² – 1/2)(b² + 1/2)= (b²)² – (1/2)² = b⁴ – 1/4
- 12. (2a/3 – 5b)(2a/3 + 5b) = (2a/3)² – (5b)²= 4a ²/9 - 25b ²
13. (2a + b)(2a – b) – (2a + b)²= (2a)² - b² - {(2a)² + 2(2a)(b) + b²} = 4a² - b² – 4a² – 4ab – b² = - 2b² - 4ab
14. (x + 5x)(x - 5x) = (x)² - (5x) ² = x ² - 25x ²
15. (- 9x – 5xy)(- 9x + 5xy) = (- 9x)² - (- 5xy)² =81x ² + 25x²y²
16. (-13n⁵p² + 1)(13n⁵p² + 1) = (1)² - (-13n⁵p²)² = 1 - 169n¹°p⁴
- 17. (1 – a)(1 + a) – (1 – 2a)(1 + 2a) = {1² – a²} – {1² – (2a)²} = 1 – a² -1 + 4a² = 3a²
18. (x² – 2xy)(x²+2xy) + (x² + 2xy)² = {(x²)² – (2xy)²} + {(x²)² + 2(x²)(2xy) + (2xy)²} = x⁴ - 4x²y² + x⁴ + 4x³y + 4x²y² = 2x⁴ +4x³y
- 19. (1 – w⁵)(1 + w⁵) = (1)² - (w⁵)² = 1 - w¹º
20. ( 3/4p⁷ – 2/5q⁴ )(3/4p⁷ + 2/5q⁴) =
= ( 3/4p⁷)² – (2/5q⁴)² =
= 9/16p¹⁴ – 4/25 q⁸
21. (abc + 4x)(abc - 4x) =
= (abc)² - (4x)²
= a²b²c² – 16x²
22. (0,05x – 2)(0,05 + 2)
= (0,05x)² – (2)²
= 0,0025 - 4
- 23. ( 6x⁵y²z³ – 1)(6x⁵y²z³ + 1)
= ( 6x⁵y²z³)² – (1)²
= 36 x¹°y⁴z⁶ - 1
- 23. (2p + q/4)(2p – q/4)
= (2p)² – (q/4)²
= 4p² – q²/16
- 24. (0,3x²y – 2z)(0,3x²y + 2z)
= (0,3x²y)² – (2z)²= 0,09x⁴y² - 4z²
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