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Claro, vamos a resolver los ejercicios aplicando la regla del binomio al cuadrado, que para [tex]\((a + b)^2\)[/tex] nos dice que se expande como [tex]\(a^2 + 2ab + b^2\)[/tex].
1. Ejercicio 9: [tex]\((x + 5)^2\)[/tex]
[tex]\[
(x + 5)^2 = x^2 + 2 \cdot x \cdot 5 + 5^2 = x^2 + 10x + 25
\][/tex]
2. Ejercicio 15: [tex]\((4x + 2y)^2\)[/tex]
[tex]\[
(4x + 2y)^2 = (4x)^2 + 2 \cdot 4x \cdot 2y + (2y)^2 = 16x^2 + 16xy + 4y^2
\][/tex]
3. Ejercicio 21: [tex]\((3x - 5)^2\)[/tex]
[tex]\[
(3x - 5)^2 = (3x)^2 + 2 \cdot 3x \cdot (-5) + (-5)^2 = 9x^2 - 30x + 25
\][/tex]
4. Ejercicio 27: [tex]\((9a - 8b)^2\)[/tex]
[tex]\[
(9a - 8b)^2 = (9a)^2 + 2 \cdot 9a \cdot (-8b) + (-8b)^2 = 81a^2 - 144ab + 64b^2
\][/tex]
5. Ejercicio 33: [tex]\((6w^4 - 3y^2)^2\)[/tex]
[tex]\[
(6w^4 - 3y^2)^2 = (6w^4)^2 + 2 \cdot 6w^4 \cdot (-3y^2) + (-3y^2)^2 = 36w^8 - 36w^4y^2 + 9y^4
\][/tex]
6. Ejercicio 10: [tex]\((a + 7)^2\)[/tex]
[tex]\[
(a + 7)^2 = a^2 + 2 \cdot a \cdot 7 + 7^2 = a^2 + 14a + 49
\][/tex]
7. Ejercicio 16: [tex]\((3a + b)^2\)[/tex]
[tex]\[
(3a + b)^2 = (3a)^2 + 2 \cdot 3a \cdot b + b^2 = 9a^2 + 6ab + b^2
\][/tex]
8. Ejercicio 22: [tex]\((9w - 32)^2\)[/tex]
[tex]\[
(9w - 32)^2 = (9w)^2 + 2 \cdot 9w \cdot (-32) + (-32)^2 = 81w^2 - 576w + 1024
\][/tex]
9. Ejercicio 28: [tex]\((7y - 8z)^2\)[/tex]
[tex]\[
(7y - 8z)^2 = (7y)^2 + 2 \cdot 7y \cdot (-8z) + (-8z)^2 = 49y^2 - 112yz + 64z^2
\][/tex]
10. Ejercicio 34: [tex]\((4x^3 - 2y^2)^2\)[/tex]
[tex]\[
(4x^3 - 2y^2)^2 = (4x^3)^2 + 2 \cdot 4x^3 \cdot (-2y^2) + (-2y^2)^2 = 16x^6 - 16x^3y^2 + 4y^4
\][/tex]
11. Ejercicio 11: [tex]\((6b + 5)^2\)[/tex]
[tex]\[
(6b + 5)^2 = (6b)^2 + 2 \cdot 6b \cdot 5 + 5^2 = 36b^2 + 60b + 25
\][/tex]
12. Ejercicio 17: [tex]\((2a + 8b)^2\)[/tex]
[tex]\[
(2a + 8b)^2 = (2a)^2 + 2 \cdot 2a \cdot 8b + (8b)^2 = 4a^2 + 32ab + 64b^2
\][/tex]
13. Ejercicio 23: [tex]\((12yz - 7xz)^2\)[/tex]
[tex]\[
(12yz - 7xz)^2 = (12yz)^2 + 2 \cdot 12yz \cdot (-7xz) + (-7xz)^2 = 144y^2z^2 - 168xyz^2 + 49x^2z^2
\][/tex]
14. Ejercicio 29: [tex]\((2x^3 + y^2)^2\)[/tex]
[tex]\[
(2x^3 + y^2)^2 = (2x^3)^2 + 2 \cdot 2x^3 \cdot y^2 + (y^2)^2 = 4x^6 + 4x^3y^2 + y^4
\][/tex]
15. Ejercicio 35: [tex]\((6y^3 + z^2)^2\)[/tex]
[tex]\[
(6y^3 + z^2)^2 = (6y^3)^2 + 2 \cdot 6y^3 \cdot z^2 + (z^2)^2 = 36y^6 + 12y^3z^2 + z^4
\][/tex]
16. Ejercicio 12: [tex]\((7x + 3)^2\)[/tex]
[tex]\[
(7x + 3)^2 = (7x)^2 + 2 \cdot 7x \cdot 3 + 3^2 = 49x^2 + 42x + 9
\][/tex]
17. Ejercicio 18: [tex]\((6y + 8z)^2\)[/tex]
[tex]\[
(6y + 8z)^2 = (6y)^2 + 2 \cdot 6y \cdot 8z + (8z)^2 = 36y^2 + 96yz + 64z^2
\][/tex]
18. Ejercicio 24: [tex]\((2a - b)^2\)[/tex]
[tex]\[
(2a - b)^2 = (2a)^2 + 2 \cdot 2a \cdot (-b) + (-b)^2 = 4a^2 - 4ab + b^2
\][/tex]
19. Ejercicio 30: [tex]\((5a^2 + b^4)^2\)[/tex]
[tex]\[
(5a^2 + b^4)^2 = (5a^2)^2 + 2 \cdot 5a^2 \cdot b^4 + (b^4)^2 = 25a^4 + 10a^2b^4 + b^8
\][/tex]
20. Ejercicio 36: [tex]\((5y^3 - 3z^2)^2\)[/tex]
[tex]\[
(5y^3 - 3z^2)^2 = (5y^3)^2 + 2 \cdot 5y^3 \cdot (-3z^2) + (-3z^2)^2 = 25y^6 - 30y^3z^2 + 9z^4
\][/tex]
21. Ejercicio 13: [tex]\((4 + 5z)^2\)[/tex]
[tex]\[
(4 + 5z)^2 = 4^2 + 2 \cdot 4 \cdot 5z + (5z)^2 = 16 + 40z + 25z^2
\][/tex]
22. Ejercicio 19: [tex]\((y - 3z)^2\)[/tex]
[tex]\[
(y - 3z)^2 = y^2 + 2 \cdot y \cdot (-3z) + (-3z)^2 = y^2 - 6yz + 9z^2
\][/tex]
23. Ejercicio 25: [tex]\((4x - 5y)^2\)[/tex]
[tex]\[
(4x - 5y)^2 = (4x)^2 + 2 \cdot 4x \cdot (-5y) + (-5y)^2 = 16x^2 - 40xy + 25y^2
\][/tex]
24. Ejercicio 31: [tex]\((3a^2 - b^4)^2\)[/tex]
[tex]\[
(3a^2 - b^4)^2 = (3a^2)^2 + 2 \cdot 3a^2 \cdot (-b^4) + (-b^4)^2 = 9a^4 - 6a^2b^4 + b^8
\][/tex]
25. Ejercicio 37: [tex]\((7w^3 + 9y^2)^2\)[/tex]
[tex]\[
(7w^3 + 9y^2)^2 = (7w^3)^2 + 2 \cdot 7w^3 \cdot 9y^2 + (9y^2)^2 = 49w^6 + 126w^3y^2 + 81y^4
\][/tex]
26. Ejercicio 14: [tex]\((2x + y)^2\)[/tex]
[tex]\[
(2x + y)^2 = (2x)^2 + 2 \cdot 2x \cdot y + y^2 = 4x^2 + 4xy + y^2
\][/tex]
27. Ejercicio 20: [tex]\((3a - 5)^2\)[/tex]
[tex]\[
(3a - 5)^2 = (3a)^2 + 2 \cdot 3a \cdot (-5) + (-5)^2 = 9a^2 - 30a + 25
\][/tex]
28. Ejercicio 26: [tex]\((3y - 4z)^2\)[/tex]
[tex]\[
(3y - 4z)^2 = (3y)^2 + 2 \cdot 3y \cdot (-4z) + (-4z)^2 = 9y^2 - 24yz + 16z^2
\][/tex]
29. Ejercicio 32: [tex]\((2x^5 + y^2)^2\)[/tex]
[tex]\[
(2x^5 + y^2)^2 = (2x^5)^2 + 2 \cdot 2x^5 \cdot y^2 + (y^2)^2 = 4x^10 + 4x^5y^2 + y^4
\][/tex]
30. Ejercicio 38: [tex]\((5x^5 - 4y^2)^2\)[/tex]
[tex]\[
(5x^5 - 4y^2)^2 = (5x^5)^2 + 2 \cdot 5x^5 \cdot (-4y^2) + (-4y^2)^2 = 25x^10 - 40x^5y^2 + 16y^4
\][/tex]
Ahí tienes cada uno de los ejercicios resueltos aplicando la regla del binomio al cuadrado.
1. Ejercicio 9: [tex]\((x + 5)^2\)[/tex]
[tex]\[
(x + 5)^2 = x^2 + 2 \cdot x \cdot 5 + 5^2 = x^2 + 10x + 25
\][/tex]
2. Ejercicio 15: [tex]\((4x + 2y)^2\)[/tex]
[tex]\[
(4x + 2y)^2 = (4x)^2 + 2 \cdot 4x \cdot 2y + (2y)^2 = 16x^2 + 16xy + 4y^2
\][/tex]
3. Ejercicio 21: [tex]\((3x - 5)^2\)[/tex]
[tex]\[
(3x - 5)^2 = (3x)^2 + 2 \cdot 3x \cdot (-5) + (-5)^2 = 9x^2 - 30x + 25
\][/tex]
4. Ejercicio 27: [tex]\((9a - 8b)^2\)[/tex]
[tex]\[
(9a - 8b)^2 = (9a)^2 + 2 \cdot 9a \cdot (-8b) + (-8b)^2 = 81a^2 - 144ab + 64b^2
\][/tex]
5. Ejercicio 33: [tex]\((6w^4 - 3y^2)^2\)[/tex]
[tex]\[
(6w^4 - 3y^2)^2 = (6w^4)^2 + 2 \cdot 6w^4 \cdot (-3y^2) + (-3y^2)^2 = 36w^8 - 36w^4y^2 + 9y^4
\][/tex]
6. Ejercicio 10: [tex]\((a + 7)^2\)[/tex]
[tex]\[
(a + 7)^2 = a^2 + 2 \cdot a \cdot 7 + 7^2 = a^2 + 14a + 49
\][/tex]
7. Ejercicio 16: [tex]\((3a + b)^2\)[/tex]
[tex]\[
(3a + b)^2 = (3a)^2 + 2 \cdot 3a \cdot b + b^2 = 9a^2 + 6ab + b^2
\][/tex]
8. Ejercicio 22: [tex]\((9w - 32)^2\)[/tex]
[tex]\[
(9w - 32)^2 = (9w)^2 + 2 \cdot 9w \cdot (-32) + (-32)^2 = 81w^2 - 576w + 1024
\][/tex]
9. Ejercicio 28: [tex]\((7y - 8z)^2\)[/tex]
[tex]\[
(7y - 8z)^2 = (7y)^2 + 2 \cdot 7y \cdot (-8z) + (-8z)^2 = 49y^2 - 112yz + 64z^2
\][/tex]
10. Ejercicio 34: [tex]\((4x^3 - 2y^2)^2\)[/tex]
[tex]\[
(4x^3 - 2y^2)^2 = (4x^3)^2 + 2 \cdot 4x^3 \cdot (-2y^2) + (-2y^2)^2 = 16x^6 - 16x^3y^2 + 4y^4
\][/tex]
11. Ejercicio 11: [tex]\((6b + 5)^2\)[/tex]
[tex]\[
(6b + 5)^2 = (6b)^2 + 2 \cdot 6b \cdot 5 + 5^2 = 36b^2 + 60b + 25
\][/tex]
12. Ejercicio 17: [tex]\((2a + 8b)^2\)[/tex]
[tex]\[
(2a + 8b)^2 = (2a)^2 + 2 \cdot 2a \cdot 8b + (8b)^2 = 4a^2 + 32ab + 64b^2
\][/tex]
13. Ejercicio 23: [tex]\((12yz - 7xz)^2\)[/tex]
[tex]\[
(12yz - 7xz)^2 = (12yz)^2 + 2 \cdot 12yz \cdot (-7xz) + (-7xz)^2 = 144y^2z^2 - 168xyz^2 + 49x^2z^2
\][/tex]
14. Ejercicio 29: [tex]\((2x^3 + y^2)^2\)[/tex]
[tex]\[
(2x^3 + y^2)^2 = (2x^3)^2 + 2 \cdot 2x^3 \cdot y^2 + (y^2)^2 = 4x^6 + 4x^3y^2 + y^4
\][/tex]
15. Ejercicio 35: [tex]\((6y^3 + z^2)^2\)[/tex]
[tex]\[
(6y^3 + z^2)^2 = (6y^3)^2 + 2 \cdot 6y^3 \cdot z^2 + (z^2)^2 = 36y^6 + 12y^3z^2 + z^4
\][/tex]
16. Ejercicio 12: [tex]\((7x + 3)^2\)[/tex]
[tex]\[
(7x + 3)^2 = (7x)^2 + 2 \cdot 7x \cdot 3 + 3^2 = 49x^2 + 42x + 9
\][/tex]
17. Ejercicio 18: [tex]\((6y + 8z)^2\)[/tex]
[tex]\[
(6y + 8z)^2 = (6y)^2 + 2 \cdot 6y \cdot 8z + (8z)^2 = 36y^2 + 96yz + 64z^2
\][/tex]
18. Ejercicio 24: [tex]\((2a - b)^2\)[/tex]
[tex]\[
(2a - b)^2 = (2a)^2 + 2 \cdot 2a \cdot (-b) + (-b)^2 = 4a^2 - 4ab + b^2
\][/tex]
19. Ejercicio 30: [tex]\((5a^2 + b^4)^2\)[/tex]
[tex]\[
(5a^2 + b^4)^2 = (5a^2)^2 + 2 \cdot 5a^2 \cdot b^4 + (b^4)^2 = 25a^4 + 10a^2b^4 + b^8
\][/tex]
20. Ejercicio 36: [tex]\((5y^3 - 3z^2)^2\)[/tex]
[tex]\[
(5y^3 - 3z^2)^2 = (5y^3)^2 + 2 \cdot 5y^3 \cdot (-3z^2) + (-3z^2)^2 = 25y^6 - 30y^3z^2 + 9z^4
\][/tex]
21. Ejercicio 13: [tex]\((4 + 5z)^2\)[/tex]
[tex]\[
(4 + 5z)^2 = 4^2 + 2 \cdot 4 \cdot 5z + (5z)^2 = 16 + 40z + 25z^2
\][/tex]
22. Ejercicio 19: [tex]\((y - 3z)^2\)[/tex]
[tex]\[
(y - 3z)^2 = y^2 + 2 \cdot y \cdot (-3z) + (-3z)^2 = y^2 - 6yz + 9z^2
\][/tex]
23. Ejercicio 25: [tex]\((4x - 5y)^2\)[/tex]
[tex]\[
(4x - 5y)^2 = (4x)^2 + 2 \cdot 4x \cdot (-5y) + (-5y)^2 = 16x^2 - 40xy + 25y^2
\][/tex]
24. Ejercicio 31: [tex]\((3a^2 - b^4)^2\)[/tex]
[tex]\[
(3a^2 - b^4)^2 = (3a^2)^2 + 2 \cdot 3a^2 \cdot (-b^4) + (-b^4)^2 = 9a^4 - 6a^2b^4 + b^8
\][/tex]
25. Ejercicio 37: [tex]\((7w^3 + 9y^2)^2\)[/tex]
[tex]\[
(7w^3 + 9y^2)^2 = (7w^3)^2 + 2 \cdot 7w^3 \cdot 9y^2 + (9y^2)^2 = 49w^6 + 126w^3y^2 + 81y^4
\][/tex]
26. Ejercicio 14: [tex]\((2x + y)^2\)[/tex]
[tex]\[
(2x + y)^2 = (2x)^2 + 2 \cdot 2x \cdot y + y^2 = 4x^2 + 4xy + y^2
\][/tex]
27. Ejercicio 20: [tex]\((3a - 5)^2\)[/tex]
[tex]\[
(3a - 5)^2 = (3a)^2 + 2 \cdot 3a \cdot (-5) + (-5)^2 = 9a^2 - 30a + 25
\][/tex]
28. Ejercicio 26: [tex]\((3y - 4z)^2\)[/tex]
[tex]\[
(3y - 4z)^2 = (3y)^2 + 2 \cdot 3y \cdot (-4z) + (-4z)^2 = 9y^2 - 24yz + 16z^2
\][/tex]
29. Ejercicio 32: [tex]\((2x^5 + y^2)^2\)[/tex]
[tex]\[
(2x^5 + y^2)^2 = (2x^5)^2 + 2 \cdot 2x^5 \cdot y^2 + (y^2)^2 = 4x^10 + 4x^5y^2 + y^4
\][/tex]
30. Ejercicio 38: [tex]\((5x^5 - 4y^2)^2\)[/tex]
[tex]\[
(5x^5 - 4y^2)^2 = (5x^5)^2 + 2 \cdot 5x^5 \cdot (-4y^2) + (-4y^2)^2 = 25x^10 - 40x^5y^2 + 16y^4
\][/tex]
Ahí tienes cada uno de los ejercicios resueltos aplicando la regla del binomio al cuadrado.
Thanks for taking the time to read RESUELVE los ejercicios aplicando la regla del binomio al cuadrado 9 tex x 5 2 tex 10 tex a 7 2 tex 11 tex 6b. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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