Álgebra básica

Un número a

a

3a, 5c, 8d

a
a
2

a a

h

b

A△ =

hb 2

3a + 7 a = 10a

aia = a 2

aic = ac

( a + b )( c + d ) ( a + b )( c + d ) = ( a + b ) c + ( a + b ) d

( a + b)( c + d ) = ( a + b ) c + ( a + b ) d ( a + b )( c + d ) = ac + bc + ad + bd

( a + bc + d )( ab + cd )

( ( a + bc ) + d ) ( ab + cd )
( a + bc + d )( ab + cd ) = ( a + bc )( ab + cd ) + d ( ab+ cd ) = ( a + bc ) ab + ( a + bc ) cd + abd + cd 2 ( ( a + bc ) + d ) ( ab + cd ) = a 2b + ab2c + acd + bc 2 d + abd + cd 2

( a + bc + d )( ab + cd ) = a 2b + ab 2c + acd + bc 2 d + abd + cd 21, 2,3, 4,5... 4, 7,10,13,16... 2, 6, 12, 20, 30...

an = n 2 + 3n, n ∈ ℕ a1 = 12 + 3i1 = 4 a2 = 22 + 3i2 = 10 a3 = 32 + 3i3 = 18 a4 = 42 + 3i4 = 4

an = n 2 + 3n bn = 3n + 2 n +1 cn = 3n ( n +1)

1, 2, 2, 4, 8, 32... 8i32 = 256

F = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...

a1 = 0 a2 = 1 an = an −1 + an − 2

a1 = 1; a2 = 2; an = ( an −1 ) + n a1 = 1; a2 = 3; an = an −1 ian − 2

21, 2, 6, 42, 1806, …

( a + b )( a − b ) + ( a + b )( a + b ) = a ( a − b ) + b ( a − b ) + a ( a + b ) + b ( a + b )
= a 2 − ab + ab − b 2 + a 2 + ab + ab + b 2

( a + b )( a − b ) + ( a + b)( a + b ) =

2a 2 + 2ab

(a + b)

2

( a + b)

2

= ( a + b )( a + b ) = a (a + b) + b (a + b) = a 2 + ab + ab + b 2

( a + b)

2

= a 2 + 2ab + b 2

( a − b) (a ± b)
2

2= a 2 ± 2ab + b 2

(a + b)

3

(a + b)

3

= ( a + b )( a + b )( a + b ) ∴ = ( a 2 + 2ab + b 2 ) ( a + b ) = a ( a 2 + 2ab + b 2 ) + b ( a 2 + 2ab + b 2 ) = a 3 + 2a 2b + ab 2 + a 2b + 2ab 2+ b3

(a + b) (a ± b)
3

3

= a 3 + 3a 2b + 3ab 2 + b3

= a 3 ± 3a 2b + 3ab 2 ± b 3

( a + b )( a − b )

( a + b )( a − b ) = a ( a − b ) + b ( a − b )
= a 2 − ab + ab − b 2

( a + b)( a − b ) =
(a + b + c)
2

a 2 − b2

(a + b + c)

2

= ( a + b + c )( a + b + c ) = a (a + b + c) + b (a + b + c) + c (a + b + c) = a 2 + ab + ac + ab + b 2 + bc + ac + bc + c 2

(a +...