POTENCIAS

EJERCICIOS DE BLADOR “211”

3. (x2 + y

3 )

6 = (x

2)

6 + 6 (x

2)

5(y

3) + 15(x

2)

4 (y

3)

2 + 20 (x

2)

3 (y

3)3 + 15 (x

2)

2 (y

3)

4 + 6(x

2) (y

3)5 + (y

3)

6

R= x12

+ 6x10

y3 + 15x

8 y

6 + 20x

6 y

9 + 15x

4 y

12 + 6x

2 y

15 + y

18

4.- (3-y7)

7= ( 3)

7 + 7 (3 )

6 (-y

7) + 21( 3)

5 (-y

7)

2 + 35( 3)

4(y

7)

3+35(3)

3 ( -y

7)

4 + 21( 3)

2 ( -y

7)

5 + 7(3)

(-y 7)

6 + ( -y

7)

7

R= 2187 – 5103y14

+ 5103y14

-2835y21

+ 945y20

-189y35

21y42

–y49

7

( - )6 = (

)

6 -6 (

)5 ( ) +15 (

)4 ( )2 -20 (

)3 ( )3 +15 (

)2 ( )4 -6(

) (

)5

+( )6

=

6 -

5 +

-

+

-

+

8

(1-x4)

8 = (1)

8 - 8(1)

7(x

4) + 28(1)

6(x

4)2 -56(1)

5(x

4)3 +70 (1)

4(x

4)4 –

56(1)3(x

4)5 + 28 (1)

2(x

4)6 – 8(1)(x

4)7 + (x

4)8

= 1-8x4+28x

8-56x

12+70x

16-56x

20 + 28x

24 – 8x

28 – x

32

9. (2/3x - 3/2 y)7=

(2/3x)7 – 7(2/3x)

6(3/2y) + 21(2/3x)

5(3/2y)

2-35(2/3x)

4(3/2y)

3+35(2/3x)

3(3/2y)

4 –

21(2/3x)2(3/2y)

5+7(2/3y)

6 – (3/2y)

7=

128/2187x7 – 224/243x

6y + 56/9x

5y

2- 70/3x

4y

3 +105/2x

3y

4 – 567/8x

2y

5 + 1701/32xy

6- 2187/128y

7

R=128/2187x7 – 224/243x6y + 56/9x5y2- 70/3x4y3 +105/2x3y4 – 567/8x2y5 + 1701/32xy6-

2187/128y7

10.-

=

11.(x3+mn)

8=

(x3)

8+ 8(x

3)

7mn+ 28(x

3)

6(mn)

2 + 56 (x

3)

5(mn)

3+70 (x

3)

4(mn)

4+ 56(x

3)

3(mn)

5 + 28(x

3)

2(mn)

6+8

(x3)(mn)

7+(mn)

8=

X24

+8x21

mn+28x18

m2n

2 + 56x

15m

3n

3 + 70x

12m

4n

4+ 56x

9m

5n

5+ 28x

6m

6n

6+ 8x

3m

7n

7+m

8n

8

R= X24+8x21mn+28x18m2n2 + 56x15m3n3 + 70x12m4n4+ 56x9m5n5+ 28x6m6n6+

8x3m7n7+m8n8

12.-

=

14.

(2m₂-5m₅)₆=(2m₂)₆

(2m₂-5n₅)₆= (2m₂)₆- 6(2m₂) 5 (5n₅)+15(2m₂)₄ (5n₅)₂ -20(2m₂)₃ (5n₅)₃+15(2m₂)₂(5n₅)₄-6(2m₂)

(5n₅)₅+(5n₅)₆

=64m₁₂-960m₁₀n₅+6000m₈n₁₀-20000m₆n₁₅+37.500m₄n₃₀-37500m₂n₂+15625n₁₀

15.

(4-x5/4)₇

=(4)₇-7(4)₆(x₅/4)+21(4)₅(x₅/4)₂-35(4)₄(x₅/4)₃+35(4)3(x₅/4)₄-21(4)₂(x₅/4)₅+7(4)(x₅/4)₆-(x₅/4)₇

=16384+7168x₅+1344x₁₀-140x₁₅+35x₂₀/4-21x₂₅/64+7x₃₀/1024-1 /16384 x₃₅