Use the binomial expansion theorem to find each term. The binomial theorem states <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>n</mi></mrow></munderover></mstyle><mo>⁡</mo><mi>n</mi><mi>C</mi><mi>k</mi><mo>⋅</mo><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi><mo>-</mo><mi>k</mi></mrow></msup><msup><mrow><mi>b</mi></mrow><mrow><mi>k</mi></mrow></msup><mo>)</mo></mrow></mstyle></math> .

Expand the summation.

Simplify the exponents for each term of the expansion.

Multiply <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mrow><mn>4</mn></mrow></msup></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn><mi>t</mi></mstyle></math> .

Rewrite using the commutative property of multiplication.

Anything raised to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><msup><mrow><mi>r</mi></mrow><mrow><mn>4</mn></mrow></msup></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Anything raised to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><msup><mrow><mi>r</mi></mrow><mrow><mn>4</mn></mrow></msup></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify.

Rewrite using the commutative property of multiplication.

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn><mi>t</mi></mstyle></math> .

Rewrite using the commutative property of multiplication.

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> .

Simplify.

Apply the product rule to <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn><mi>t</mi></mstyle></math> .

Rewrite using the commutative property of multiplication.

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>27</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mrow><mn>0</mn></mrow></msup></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Anything raised to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mo>-</mo><mn>3</mn><mi>t</mi><mo>)</mo></mrow><mrow><mn>4</mn></mrow></msup></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Do you know how to Expand Using the Binomial Theorem (r-3t)^4? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | eight hundred twenty million eight hundred eighty-five thousand two hundred thirty-two |
---|

- 820885232 has 32 divisors, whose sum is
**4155731568** - The reverse of 820885232 is
**232588028** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 38
- Digital Root 2

Name | one billion five million six hundred four thousand six hundred eighty-nine |
---|

- 1005604689 has 32 divisors, whose sum is
**1416499200** - The reverse of 1005604689 is
**9864065001** - Previous prime number is
**23**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 39
- Digital Root 3

Name | two billion seventy-three million three hundred eleven thousand two hundred one |
---|

- 2073311201 has 4 divisors, whose sum is
**2232796692** - The reverse of 2073311201 is
**1021133702** - Previous prime number is
**13**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 20
- Digital Root 2