(2 + x)² - Inicio MATE

ALGEBRA
EJERCICIOS RESUELTOS
EJERCICIOS BINOMIO AL CUADRADO.
1. (2 + x)² = 2² + 2(2)(x) + x² = 4 + 4x + x
2. (3a – 5b)² = (3a)² - 2(3a)(5b) + (5b)²
= 9a² - 30ab + 25b²
3. (x + y)² = x² + 2 (x)(y) + y² = x² + 2xy + y²
4. (p - q)² = p² - 2pq + q²
5. (2p + q)² = (2p)² + 2(2p)(q) + q² = 4p² + 4pq + q²
6. (3a + b)² = (3a)² + 2(3a)(b) + b² = 9a² + 6ab + b²
7. (2a - 3b)² = (2a)² - 2(2a)(3b) + (3b)² = 4a² - 12ab + 9b²
8. (x + 1)² = x² + 2(x)(1) + (1)² = x² + 2x + 1
9.
(a - 6)² = (a)² - 2(a)(6) + (6)² = a² - 12a + 36
10. (x + 9)² = (x)² + 2(x)(9) + (9)² = x² + 18x + 81
11. (3p - 1)² = (3p)² - 2(3p)(1) + (1)² = 9p² - 6p + 1
12. (x + 5)² = (x)² + 3(x)(5) + (5)² = x² + 15x + 25
13. (6x – 5y)² = (6x)² - 2(6x)(5y) + (5y)² = 36x² - 60xy + 25y²
13. (2m – 1)² = (2m)² - 2(2m)(1) + (1)² = 4m² - 4m + 1
14. (4pq - 3q)² = (4pq)² - 2(4pq)(3q) + (3q)² = 16 p² q² – 24pq² + 9q²
15. (9x2 – 7y2)² = (9x²)² - 2(9x²)(7y²) + (7y²)²
= 81x4 - 126 x²y² +
49y4
16. (8a2b + 7ab6y²)² = (8a²b)² + 2(8a²b)(7ab6y²) + (7ab6y²)² =
64a4b² + 112a3b7y² + 49a²b12y4
17. (15x²y - 3xy²z6)² = (15x²y)² - 2(15x²y)(3xy²z6) + (3x²z6)²=
225x4y² - 90x²y3z6 + 9x4z12
18. (2a - 3b)² + (3a - 5b)² = (4a²-2(2a)(3b)+(9b²) [(3a)²2(3a)(5b)+ (5b)²]= 16a² - 12ab + 6b² + 9a² - 30ab + 25b²= 25a² - 42ab + 31b²
19. (11x - 5y)² - (13x + 3y)² + (x - 2y)²
=(121x² - 2(11x)(5y) + 25y²) - (169x²+ 2 (13x)(3y) + 9y²) + (x² - 2(x)(2y)
+ 4y²) = 121x² - 110xy + 25y² - 169x² - 78xy - 9y² + x² - 4xy + 4y² = 47x² - 192xy - 20y²
20. [a/2 + 2b]² + [2a – b/2]² =[(a²/4+2(a/2(2b)+4b²]+[4a²2(2a)(b/2+b²/4]
= a²/4 + 4ab/² + 4b² + 4a² - 4ab/2 + b² /4
= a²/4 + 8ab + 4b² + b²/4
= a² + 16a² /4 + 16b² + b²/4
= 17a²/4 + 17b²/4
21. (3a - b/5)² = 9a² - 2(3a)(b/5) + b²/25
= 9a²- 6ab/5 + b²/25
(2x²/3 - 3yz/5)² =
= 4x4 /9 - 2(2x²/3)(3yz/5) + (9x²y²/25)
= 4x4 /9 - 12x²yz/15 + 9x²y²/25
= 4x4 /9 - 4x²yz/5 + 9x²y²/25
22. (11x - 5y)² - (13x + 3y)² + (x - 2y)²=
= (121x² - 2(11x)(5y) + 25y²) - (169x²+ 2 (13x)(3y) + 9y²) + (x² - 2(x)(2y) + 4y²)
= 121x² - 110xy + 25y² - 169x² - 78xy - 9y² + x² - 4xy + 4y²
= - 47x² - 192xy - 20y²
23. [a/2 + 2b]² + [2a – b/2]² =[(a²/4+2(a/2(2b)+4b²]+[4a²2(2a)(b/2+b²/4]
= a²/4 + 4ab/² + 4b² + 4a² - 4ab/2 + b² /4
= a²/4 + 8ab + 4b² + b²/4
= a² + 16a² /4 + 16b² + b²/4
= 17a²/4 + 17b²/4
24. (3a - b/5)² = 9a² - 2(3a)(b/5) + b²/25
= 9a²- 6ab/5 + b²/25