Pré-cálculo Exemplos

${(2 x - 3 y)}^{11}$

Etapa 1

O triângulo de Pascal pode ser exibido assim:

$1$

$1 - 1$

$1 - 2 - 1$

$\dots$

$1 - 9 - 36 - 84 - 126 - 126 - 84 - 36 - 9 - 1$

$1 - 10 - 45 - 120 - 210 - 252 - 210 - 120 - 45 - 10 - 1$

$1 - 11 - 55 - 165 - 330 - 462 - 462 - 330 - 165 - 55 - 11 - 1$

O triângulo pode ser usado para calcular os coeficientes da expansão de ${(a + b)}^{n}$ , usando o expoente $n$ e somando $1$ . Os coeficientes corresponderão à linha $n + 1$ do triângulo. Para ${(2 x - 3 y)}^{11}$ , $n = 11$ , de forma que os coeficientes da expansão corresponderão à linha $12$ .

Etapa 2

A expansão segue a regra ${(a + b)}^{n} = c_{0} a^{n} b^{0} + c_{1} a^{n - 1} b^{1} + c_{n - 1} a^{1} b^{n - 1} + c_{n} a^{0} b^{n}$ . Os valores dos coeficientes, do triângulo, são $1 - 11 - 55 - 165 - 330 - 462 - 462 - 330 - 165 - 55 - 11 - 1$ .

$1 a^{11} b^{0} + 11 a^{10} b + 55 a^{9} b^{2} + 165 a^{8} b^{3} + 330 a^{7} b^{4} + 462 a^{6} b^{5} + 462 a^{5} b^{6} + 330 a^{4} b^{7} + 165 a^{3} b^{8} + 55 a^{2} b^{9} + 11 a b^{10} + 1 a^{0} b^{11}$

Etapa 3

Substitua os valores reais de $a$ $2 x$ e $b$ $- 3 y$ na expressão.

$1 {(2 x)}^{11} {(- 3 y)}^{0} + 11 {(2 x)}^{10} {(- 3 y)}^{1} + 55 {(2 x)}^{9} {(- 3 y)}^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4

Simplifique cada termo.

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Etapa 4.1

Multiplique ${(2 x)}^{11}$ por $1$ .

${(2 x)}^{11} {(- 3 y)}^{0} + 11 {(2 x)}^{10} {(- 3 y)}^{1} + 55 {(2 x)}^{9} {(- 3 y)}^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.2

Aplique a regra do produto a $2 x$ .

$2^{11} x^{11} {(- 3 y)}^{0} + 11 {(2 x)}^{10} {(- 3 y)}^{1} + 55 {(2 x)}^{9} {(- 3 y)}^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.3

Eleve $2$ à potência de $11$ .

$2048 x^{11} {(- 3 y)}^{0} + 11 {(2 x)}^{10} {(- 3 y)}^{1} + 55 {(2 x)}^{9} {(- 3 y)}^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.4

Aplique a regra do produto a $- 3 y$ .

$2048 x^{11} ({(- 3)}^{0} y^{0}) + 11 {(2 x)}^{10} {(- 3 y)}^{1} + 55 {(2 x)}^{9} {(- 3 y)}^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.5

Reescreva usando a propriedade comutativa da multiplicação.

$2048 \cdot {(- 3)}^{0} x^{11} y^{0} + 11 {(2 x)}^{10} {(- 3 y)}^{1} + 55 {(2 x)}^{9} {(- 3 y)}^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.6

Qualquer coisa elevada a $0$ é $1$ .

$2048 \cdot 1 x^{11} y^{0} + 11 {(2 x)}^{10} {(- 3 y)}^{1} + 55 {(2 x)}^{9} {(- 3 y)}^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.7

Multiplique $2048$ por $1$ .

$2048 x^{11} y^{0} + 11 {(2 x)}^{10} {(- 3 y)}^{1} + 55 {(2 x)}^{9} {(- 3 y)}^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.8

Qualquer coisa elevada a $0$ é $1$ .

$2048 x^{11} \cdot 1 + 11 {(2 x)}^{10} {(- 3 y)}^{1} + 55 {(2 x)}^{9} {(- 3 y)}^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.9

Multiplique $2048$ por $1$ .

$2048 x^{11} + 11 {(2 x)}^{10} {(- 3 y)}^{1} + 55 {(2 x)}^{9} {(- 3 y)}^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.10

Aplique a regra do produto a $2 x$ .

$2048 x^{11} + 11 (2^{10} x^{10}) {(- 3 y)}^{1} + 55 {(2 x)}^{9} {(- 3 y)}^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.11

Eleve $2$ à potência de $10$ .

$2048 x^{11} + 11 (1024 x^{10}) {(- 3 y)}^{1} + 55 {(2 x)}^{9} {(- 3 y)}^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.12

Multiplique $1024$ por $11$ .

$2048 x^{11} + 11264 x^{10} {(- 3 y)}^{1} + 55 {(2 x)}^{9} {(- 3 y)}^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.13

Simplifique.

$2048 x^{11} + 11264 x^{10} (- 3 y) + 55 {(2 x)}^{9} {(- 3 y)}^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.14

Reescreva usando a propriedade comutativa da multiplicação.

$2048 x^{11} + 11264 \cdot - 3 x^{10} y + 55 {(2 x)}^{9} {(- 3 y)}^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.15

Multiplique $11264$ por $- 3$ .

$2048 x^{11} - 33792 x^{10} y + 55 {(2 x)}^{9} {(- 3 y)}^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.16

Aplique a regra do produto a $2 x$ .

$2048 x^{11} - 33792 x^{10} y + 55 (2^{9} x^{9}) {(- 3 y)}^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.17

Eleve $2$ à potência de $9$ .

$2048 x^{11} - 33792 x^{10} y + 55 (512 x^{9}) {(- 3 y)}^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.18

Multiplique $512$ por $55$ .

$2048 x^{11} - 33792 x^{10} y + 28160 x^{9} {(- 3 y)}^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.19

Aplique a regra do produto a $- 3 y$ .

$2048 x^{11} - 33792 x^{10} y + 28160 x^{9} ({(- 3)}^{2} y^{2}) + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.20

Reescreva usando a propriedade comutativa da multiplicação.

$2048 x^{11} - 33792 x^{10} y + 28160 \cdot {(- 3)}^{2} x^{9} y^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.21

Eleve $- 3$ à potência de $2$ .

$2048 x^{11} - 33792 x^{10} y + 28160 \cdot 9 x^{9} y^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.22

Multiplique $28160$ por $9$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} + 165 {(2 x)}^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.23

Aplique a regra do produto a $2 x$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} + 165 (2^{8} x^{8}) {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.24

Eleve $2$ à potência de $8$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} + 165 (256 x^{8}) {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.25

Multiplique $256$ por $165$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} + 42240 x^{8} {(- 3 y)}^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.26

Aplique a regra do produto a $- 3 y$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} + 42240 x^{8} ({(- 3)}^{3} y^{3}) + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.27

Reescreva usando a propriedade comutativa da multiplicação.

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} + 42240 \cdot {(- 3)}^{3} x^{8} y^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.28

Eleve $- 3$ à potência de $3$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} + 42240 \cdot - 27 x^{8} y^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.29

Multiplique $42240$ por $- 27$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 330 {(2 x)}^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.30

Aplique a regra do produto a $2 x$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 330 (2^{7} x^{7}) {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.31

Eleve $2$ à potência de $7$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 330 (128 x^{7}) {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.32

Multiplique $128$ por $330$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 42240 x^{7} {(- 3 y)}^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.33

Aplique a regra do produto a $- 3 y$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 42240 x^{7} ({(- 3)}^{4} y^{4}) + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.34

Reescreva usando a propriedade comutativa da multiplicação.

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 42240 \cdot {(- 3)}^{4} x^{7} y^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.35

Eleve $- 3$ à potência de $4$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 42240 \cdot 81 x^{7} y^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.36

Multiplique $42240$ por $81$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} + 462 {(2 x)}^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.37

Aplique a regra do produto a $2 x$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} + 462 (2^{6} x^{6}) {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.38

Eleve $2$ à potência de $6$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} + 462 (64 x^{6}) {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.39

Multiplique $64$ por $462$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} + 29568 x^{6} {(- 3 y)}^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.40

Aplique a regra do produto a $- 3 y$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} + 29568 x^{6} ({(- 3)}^{5} y^{5}) + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.41

Reescreva usando a propriedade comutativa da multiplicação.

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} + 29568 \cdot {(- 3)}^{5} x^{6} y^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.42

Eleve $- 3$ à potência de $5$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} + 29568 \cdot - 243 x^{6} y^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.43

Multiplique $29568$ por $- 243$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 462 {(2 x)}^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.44

Aplique a regra do produto a $2 x$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 462 (2^{5} x^{5}) {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.45

Eleve $2$ à potência de $5$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 462 (32 x^{5}) {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.46

Multiplique $32$ por $462$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 14784 x^{5} {(- 3 y)}^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.47

Aplique a regra do produto a $- 3 y$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 14784 x^{5} ({(- 3)}^{6} y^{6}) + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.48

Reescreva usando a propriedade comutativa da multiplicação.

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 14784 \cdot {(- 3)}^{6} x^{5} y^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.49

Eleve $- 3$ à potência de $6$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 14784 \cdot 729 x^{5} y^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.50

Multiplique $14784$ por $729$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} + 330 {(2 x)}^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.51

Aplique a regra do produto a $2 x$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} + 330 (2^{4} x^{4}) {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.52

Eleve $2$ à potência de $4$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} + 330 (16 x^{4}) {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.53

Multiplique $16$ por $330$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} + 5280 x^{4} {(- 3 y)}^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.54

Aplique a regra do produto a $- 3 y$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} + 5280 x^{4} ({(- 3)}^{7} y^{7}) + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.55

Reescreva usando a propriedade comutativa da multiplicação.

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} + 5280 \cdot {(- 3)}^{7} x^{4} y^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.56

Eleve $- 3$ à potência de $7$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} + 5280 \cdot - 2187 x^{4} y^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.57

Multiplique $5280$ por $- 2187$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 165 {(2 x)}^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.58

Aplique a regra do produto a $2 x$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 165 (2^{3} x^{3}) {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.59

Eleve $2$ à potência de $3$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 165 (8 x^{3}) {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.60

Multiplique $8$ por $165$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 1320 x^{3} {(- 3 y)}^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.61

Aplique a regra do produto a $- 3 y$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 1320 x^{3} ({(- 3)}^{8} y^{8}) + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.62

Reescreva usando a propriedade comutativa da multiplicação.

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 1320 \cdot {(- 3)}^{8} x^{3} y^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.63

Eleve $- 3$ à potência de $8$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 1320 \cdot 6561 x^{3} y^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.64

Multiplique $1320$ por $6561$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} + 55 {(2 x)}^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.65

Aplique a regra do produto a $2 x$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} + 55 (2^{2} x^{2}) {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.66

Eleve $2$ à potência de $2$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} + 55 (4 x^{2}) {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.67

Multiplique $4$ por $55$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} + 220 x^{2} {(- 3 y)}^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.68

Aplique a regra do produto a $- 3 y$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} + 220 x^{2} ({(- 3)}^{9} y^{9}) + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.69

Reescreva usando a propriedade comutativa da multiplicação.

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} + 220 \cdot {(- 3)}^{9} x^{2} y^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.70

Eleve $- 3$ à potência de $9$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} + 220 \cdot - 19683 x^{2} y^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.71

Multiplique $220$ por $- 19683$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} - 4330260 x^{2} y^{9} + 11 {(2 x)}^{1} {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.72

Simplifique.

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} - 4330260 x^{2} y^{9} + 11 (2 x) {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.73

Multiplique $2$ por $11$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} - 4330260 x^{2} y^{9} + 22 x {(- 3 y)}^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.74

Aplique a regra do produto a $- 3 y$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} - 4330260 x^{2} y^{9} + 22 x ({(- 3)}^{10} y^{10}) + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.75

Reescreva usando a propriedade comutativa da multiplicação.

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} - 4330260 x^{2} y^{9} + 22 \cdot {(- 3)}^{10} x y^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.76

Eleve $- 3$ à potência de $10$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} - 4330260 x^{2} y^{9} + 22 \cdot 59049 x y^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.77

Multiplique $22$ por $59049$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} - 4330260 x^{2} y^{9} + 1299078 x y^{10} + 1 {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.78

Multiplique ${(2 x)}^{0}$ por $1$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} - 4330260 x^{2} y^{9} + 1299078 x y^{10} + {(2 x)}^{0} {(- 3 y)}^{11}$

Etapa 4.79

Aplique a regra do produto a $2 x$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} - 4330260 x^{2} y^{9} + 1299078 x y^{10} + 2^{0} x^{0} {(- 3 y)}^{11}$

Etapa 4.80

Qualquer coisa elevada a $0$ é $1$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} - 4330260 x^{2} y^{9} + 1299078 x y^{10} + 1 x^{0} {(- 3 y)}^{11}$

Etapa 4.81

Multiplique $x^{0}$ por $1$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} - 4330260 x^{2} y^{9} + 1299078 x y^{10} + x^{0} {(- 3 y)}^{11}$

Etapa 4.82

Qualquer coisa elevada a $0$ é $1$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} - 4330260 x^{2} y^{9} + 1299078 x y^{10} + 1 {(- 3 y)}^{11}$

Etapa 4.83

Multiplique ${(- 3 y)}^{11}$ por $1$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} - 4330260 x^{2} y^{9} + 1299078 x y^{10} + {(- 3 y)}^{11}$

Etapa 4.84

Aplique a regra do produto a $- 3 y$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} - 4330260 x^{2} y^{9} + 1299078 x y^{10} + {(- 3)}^{11} y^{11}$

Etapa 4.85

Eleve $- 3$ à potência de $11$ .

$2048 x^{11} - 33792 x^{10} y + 253440 x^{9} y^{2} - 1140480 x^{8} y^{3} + 3421440 x^{7} y^{4} - 7185024 x^{6} y^{5} + 10777536 x^{5} y^{6} - 11547360 x^{4} y^{7} + 8660520 x^{3} y^{8} - 4330260 x^{2} y^{9} + 1299078 x y^{10} - 177147 y^{11}$