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>x</mi><mo>)</mo></mrow><mrow><mn>2</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><mi>y</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>x</mi></mrow><mrow><mn>2</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>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify.

Simplify.

Rewrite using the commutative property of multiplication.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mi>x</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><mi>y</mi><mo>)</mo></mrow><mrow><mn>2</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><mi>y</mi></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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

- 1993586644 has 32 divisors, whose sum is
**5127595776** - The reverse of 1993586644 is
**4466853991** - Previous prime number is
**7213**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 55
- Digital Root 1

Name | two billion eight million three hundred fifty thousand four hundred eighty-six |
---|

- 2008350486 has 8 divisors, whose sum is
**3347250840** - The reverse of 2008350486 is
**6840538002** - Previous prime number is
**9**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 36
- Digital Root 9

Name | one billion one hundred sixty-seven million one hundred seventy-nine thousand five hundred seventy-five |
---|

- 1167179575 has 8 divisors, whose sum is
**1170969696** - The reverse of 1167179575 is
**5759717611** - Previous prime number is
**1061**

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