Question

1/a²-ab + 1/ab - a²+b²/a³b-ab³ la respuesta por favor con procedimiento ​

Answer 1

HOLA!

1.Sea, a = xy ; b 7

(a+b)², es un binomio cuadrado: a²+2ab+b²

Sustituyo a y b;

(xy+7)² = (xy)²+2(x)(7)+(7)²

(xy+7)² = x²y² + 14x +49

(a-b)², es un  binomio de la resta al cuadrado: a²-2ab+b²

(xy-7)² = (xy)²-2(x)(7)+(7)²

(xy-7)² = x²y² - 14x +49

(a+b)³, es binomio al cubo: a³+b³+3ab(a+b)

(xy+7)³ = (xy)³+(7)³+3(xy)(7)(xy+7)

(xy+7)² = x³y³ + 343 + 21xy(xy+7)

(a-b)³, es binomio de la resta al cubo: a³-b³-3ab(a-b)

(xy-7)³ = (xy)³-(7)³-3(xy)(7)(xy-7)

(xy-7)² = x³y³ - 343 - 21xy(xy-7)

(a+b)(a-b), es un binomio conjugado: a²-b²

(xy+7)(xy-7) = (xy)²- (7)²

(xy+7)(xy-7) = x²y² - 49

2. Sea, a = -1 ; b = a²

(a+b)², es un binomio cuadrado: a²+2ab+b²

Sustituyo a y b;

(-1+a²)² = (-1)²+2(-1)(a²)+(a²)²

(-1+a²)² = 1 - 2a² + a^4

(a-b)², es un binomio de la resta al cuadrado: a²-2ab+b²

(-1-a²)² = (-1)²-2(-1)(a²)+(a²)²

(-1-a²)² = 1 + 2a² + a^4

(a+b)³, es binomio al cubo: a³+b³+3ab(a+b)

(-1+a²)³ = (-1)³+(a²)³+3(-1)(a²)(-1+a²)

(-1+a²)³ = -1 +a^6 -3a²(-1+a²)

(a-b)³, es binomio de la resta al cubo: a³-b³-3ab(a-b)

(-1-a²)³ = (-1)³-(a²)³-3(-1)(a²)(-1+a²)

(-1-a²)² = -1 -a^6 + 3a²(-1-a²)

(a+b)(a-b), es un binomio conjugado: a²-b²

(-1+a²)(-1-a²) = (-1)²- (a²)²

(-1+a²)(-1-a²) = 1 - a^4

3. Sea, a = 6a²b ; b = 5

(a+b)², es un binomio cuadrado: a²+2ab+b²

Sustituyo a y b;

(6a²b+5)² = (6a²b)²+2(6a²b)(5)+(5)²

(6a²b+5)²= 36b²a^4 + 60a²b + 25

(a-b)², es un binomio de la resta al cuadrado: a²-2ab+b²

(6a²b-5)² = (6a²b)²-2(6a²b)(5)+(5)²

(6a²b-5)²= 36b²a^4 - 60a²b + 25  

(a+b)³, es binomio al cubo: a³+b³+3ab(a+b)

(6a²b+5)³ = (6a²b)³+(5)³+3(6a²b)(5)(6a²b+5)

(6a²b+5)³ = 216b³a^6 +125 + 90a²b(6a²b+5)

(a-b)³, es binomio de la resta al cubo: a³-b³-3ab(a-b)

(6a²b-5)³ = (6a²b)³-(5)³-3(6a²b)(5)(6a²b-5)

(6a²b-5)³ = 216b³a^6 - 125 - 90a²b(6a²b-5)

(a+b)(a-b), es un binomio conjugado: a²-b²

(6a²b+5)(6a²b-5) = (6a²b)²- (5)²

(6a²b+5)(6a²b-5) = 36b²a^4 -25

4. Sea, a = 9a^5; b = 6c²

(a+b)², es un binomio cuadrado: a²+2ab+b²

Sustituyo a y b;

(9a^5+6c²)² = (9a^5)²+2(9a^5)(6c²)+(6c²)²

(9a^5+6c²)² = 81a^10 + 108 c²a^5 + 36c^4

(a-b)², es un binomio de la resta al cuadrado: a²-2ab+b²

(9a^5-6c²)² = (9a^5)²-2(9a^5)(6c²)+(6c²)²

(9a^5-6c²)² = 81a^10 - 108 c²a^5 + 36c^4

(a+b)³, es binomio al cubo: a³+b³+3ab(a+b)

(9a^5+6c²)³ = (9a^5)³+ (6c²)³+3(9a^5)( 6c²)( 9a^5+6c²)

(9a^5+6c²)³ = 729a^15 +216c^6 + 162c²a^5 (9a^5+6c)

(a-b)³, es binomio de la resta al cubo: a³-b³-3ab(a-b)

(9a^5-6c²)³ = (9a^5)³- (6c²)³-3(9a^5)( 6c²)( 9a^5-6c²)

(9a^5-6c²)³ = 729a^15 - 216c^6 - 162c²a^5 (9a^5-6c)

(a+b)(a-b), es un binomio conjugado: a²-b²

(9a^5-6c²)(9a^5-6c²) = (9a^5)²- (6c²)²

(9a^5-6c²)(9a^5-6c²) = 81a^10 - 36c^4

5. Sea, a = 10st; b = s²v³

(a+b)², es un binomio cuadrado: a²+2ab+b²

Sustituyo a y b;

(10st+ s²v³)² = (10st)²+2(10st)( s²v³)+( s²v³)²

(10st+ s²v³)² = 100s²t² + 20ts³v³ + s^4v^6

(a-b)², es un binomio de la resta al cuadrado: a²-2ab+b²

(10st- s²v³)² = (10st)²-2(10st)( s²v³)-( s²v³)²

(10st- s²v³)² = 100s²t² - 20ts³v³ - s^4v^6

(a+b)³, es binomio al cubo: a³+b³+3ab(a+b)

(10st + s²v³)³ = (10st)³+ (s²v³)³+3(10st)( s²v³)( 10st+ s²v³)

(10st + s²v³)³ = 10³s³t³ +s^6v^9 + 30ts³v³ (10st+ s²v³)

(a-b)³, es binomio de la resta al cubo: a³-b³-3ab(a-b)

(10st - s²v³)³ = (10st)³- (s²v³)³-3(10st)( s²v³)( 10st- s²v³)

(10st - s²v³)³ = 10³s³t³ - s^6v^9 - 30ts³v³ (10st- s²v³)

(a+b)(a-b), es un binomio conjugado: a²-b²

(10st + s²v³)(10st - s²v³) = (10st)²- (s²v³)²

(10st + s²v³)(10st - s²v³) = 100s²t² - s^4v^6

6. Sea, a = a³b^4 ; b = -5

(a+b)², es un binomio cuadrado: a²+2ab+b²

Sustituyo a y b;

(a³b^4 + (-5))² = (a³b^4)²+2(a³b^4)(-5)+(-5)²

(a³b^4 - 5)² = a^6b^8 - 10 a³b^4 + 25

(a-b)², es un binomio de la resta al cuadrado: a²-2ab+b²

(a³b^4 - (-5))² = (a³b^4)²-2(a³b^4)(-5)+(-5)²

(a³b^4 + 5)² = a^6b^8 + 10 a³b^4 + 25

(a+b)³, es binomio al cubo: a³+b³+3ab(a+b)

(a³b^4 + (-5))³ = (a³b^4)³+ (-5)³+3(a³b^4)(-5)( a³b^4-5)

(a³b^4 - 5)³ = a^9b^12 – 25 -15a³ b^4(a³b^4-5)

(a-b)³, es binomio de la resta al cubo: a³-b³-3ab(a-b)

(a³b^4 - (-5))³ = (a³b^4)³- (-5)³-3(a³b^4)(-5)( a³b^4-(-5))

(a³b^4 + 5)³ = a^9b^12 + 25 +15a³ b^4(a³b^4+5)

7. Sea, a = 5ef^4 ; b = 8c

(a+b)², es un binomio cuadrado: a²+2ab+b²