Expand (3-x)^6 - Math solver

${(3 - x)}^{6}$

Use the Binomial Theorem.

$3^{6} + 6 \cdot 3^{5} (- x) + 15 \cdot 3^{4} {(- x)}^{2} + 20 \cdot 3^{3} {(- x)}^{3} + 15 \cdot 3^{2} {(- x)}^{4} + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Simplify each term.

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Raise $3$ to the power of $6$ .

$729 + 6 \cdot 3^{5} (- x) + 15 \cdot 3^{4} {(- x)}^{2} + 20 \cdot 3^{3} {(- x)}^{3} + 15 \cdot 3^{2} {(- x)}^{4} + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Raise $3$ to the power of $5$ .

$729 + 6 \cdot 243 (- x) + 15 \cdot 3^{4} {(- x)}^{2} + 20 \cdot 3^{3} {(- x)}^{3} + 15 \cdot 3^{2} {(- x)}^{4} + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Multiply $6$ by $243$ .

$729 + 1458 (- x) + 15 \cdot 3^{4} {(- x)}^{2} + 20 \cdot 3^{3} {(- x)}^{3} + 15 \cdot 3^{2} {(- x)}^{4} + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Multiply $- 1$ by $1458$ .

$729 - 1458 x + 15 \cdot 3^{4} {(- x)}^{2} + 20 \cdot 3^{3} {(- x)}^{3} + 15 \cdot 3^{2} {(- x)}^{4} + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Raise $3$ to the power of $4$ .

$729 - 1458 x + 15 \cdot 81 {(- x)}^{2} + 20 \cdot 3^{3} {(- x)}^{3} + 15 \cdot 3^{2} {(- x)}^{4} + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Multiply $15$ by $81$ .

$729 - 1458 x + 1215 {(- x)}^{2} + 20 \cdot 3^{3} {(- x)}^{3} + 15 \cdot 3^{2} {(- x)}^{4} + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Apply the product rule to $- x$ .

$729 - 1458 x + 1215 ({(- 1)}^{2} x^{2}) + 20 \cdot 3^{3} {(- x)}^{3} + 15 \cdot 3^{2} {(- x)}^{4} + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Raise $- 1$ to the power of $2$ .

$729 - 1458 x + 1215 (1 x^{2}) + 20 \cdot 3^{3} {(- x)}^{3} + 15 \cdot 3^{2} {(- x)}^{4} + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Multiply $x^{2}$ by $1$ .

$729 - 1458 x + 1215 x^{2} + 20 \cdot 3^{3} {(- x)}^{3} + 15 \cdot 3^{2} {(- x)}^{4} + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Raise $3$ to the power of $3$ .

$729 - 1458 x + 1215 x^{2} + 20 \cdot 27 {(- x)}^{3} + 15 \cdot 3^{2} {(- x)}^{4} + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Multiply $20$ by $27$ .

$729 - 1458 x + 1215 x^{2} + 540 {(- x)}^{3} + 15 \cdot 3^{2} {(- x)}^{4} + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Apply the product rule to $- x$ .

$729 - 1458 x + 1215 x^{2} + 540 ({(- 1)}^{3} x^{3}) + 15 \cdot 3^{2} {(- x)}^{4} + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Raise $- 1$ to the power of $3$ .

$729 - 1458 x + 1215 x^{2} + 540 (- x^{3}) + 15 \cdot 3^{2} {(- x)}^{4} + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Multiply $- 1$ by $540$ .

$729 - 1458 x + 1215 x^{2} - 540 x^{3} + 15 \cdot 3^{2} {(- x)}^{4} + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Raise $3$ to the power of $2$ .

$729 - 1458 x + 1215 x^{2} - 540 x^{3} + 15 \cdot 9 {(- x)}^{4} + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Multiply $15$ by $9$ .

$729 - 1458 x + 1215 x^{2} - 540 x^{3} + 135 {(- x)}^{4} + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Apply the product rule to $- x$ .

$729 - 1458 x + 1215 x^{2} - 540 x^{3} + 135 ({(- 1)}^{4} x^{4}) + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Raise $- 1$ to the power of $4$ .

$729 - 1458 x + 1215 x^{2} - 540 x^{3} + 135 (1 x^{4}) + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Multiply $x^{4}$ by $1$ .

$729 - 1458 x + 1215 x^{2} - 540 x^{3} + 135 x^{4} + 6 \cdot 3 {(- x)}^{5} + {(- x)}^{6}$

Multiply $6$ by $3$ .

$729 - 1458 x + 1215 x^{2} - 540 x^{3} + 135 x^{4} + 18 {(- x)}^{5} + {(- x)}^{6}$

Apply the product rule to $- x$ .

$729 - 1458 x + 1215 x^{2} - 540 x^{3} + 135 x^{4} + 18 ({(- 1)}^{5} x^{5}) + {(- x)}^{6}$

Raise $- 1$ to the power of $5$ .

$729 - 1458 x + 1215 x^{2} - 540 x^{3} + 135 x^{4} + 18 (- x^{5}) + {(- x)}^{6}$

Multiply $- 1$ by $18$ .

$729 - 1458 x + 1215 x^{2} - 540 x^{3} + 135 x^{4} - 18 x^{5} + {(- x)}^{6}$

Apply the product rule to $- x$ .

$729 - 1458 x + 1215 x^{2} - 540 x^{3} + 135 x^{4} - 18 x^{5} + {(- 1)}^{6} x^{6}$

Raise $- 1$ to the power of $6$ .

$729 - 1458 x + 1215 x^{2} - 540 x^{3} + 135 x^{4} - 18 x^{5} + 1 x^{6}$

Multiply $x^{6}$ by $1$ .

$729 - 1458 x + 1215 x^{2} - 540 x^{3} + 135 x^{4} - 18 x^{5} + x^{6}$

Expand (3-x)^6

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