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 hundred twenty-eight million one hundred fifty-five thousand one hundred ninety-two |
---|

- 128155192 has 64 divisors, whose sum is
**475600896** - The reverse of 128155192 is
**291551821** - Previous prime number is
**127**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 34
- Digital Root 7

Name | two billion seventy-five million nine hundred twenty-eight thousand nine hundred seventy |
---|

- 2075928970 has 8 divisors, whose sum is
**3736672164** - The reverse of 2075928970 is
**0798295702** - Previous prime number is
**5**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 49
- Digital Root 4

Name | eight hundred sixty-nine million six hundred ninety-one thousand four hundred fifty-three |
---|

- 869691453 has 8 divisors, whose sum is
**1196994816** - The reverse of 869691453 is
**354196968** - Previous prime number is
**31**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 51
- Digital Root 6