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 | one billion nine hundred fifty-five million forty-three thousand six hundred four |
---|

- 1955043604 has 16 divisors, whose sum is
**4399955136** - The reverse of 1955043604 is
**4063405591** - Previous prime number is
**4111**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 37
- Digital Root 1

Name | one hundred sixty-nine million three hundred eighty-six thousand eighty-eight |
---|

- 169386088 has 32 divisors, whose sum is
**585622548** - The reverse of 169386088 is
**880683961** - Previous prime number is
**41**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 49
- Digital Root 4

Name | one billion five hundred seventy-eight million three hundred ninety-three thousand nine hundred forty-five |
---|

- 1578393945 has 8 divisors, whose sum is
**1792744200** - The reverse of 1578393945 is
**5493938751** - Previous prime number is
**45**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 54
- Digital Root 9