Verify the Identity x^3-2=(x- cube root of 2)(x^2+ cube root of 2x+ cube root of 4)

Simplify <math><mstyle displaystyle="true"><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mroot><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mroot><mo>)</mo></mrow><mrow><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mroot><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mroot><mi>x</mi><mo>+</mo><mroot><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mroot><mo>)</mo></mrow></mstyle></math> .

Expand <math><mstyle displaystyle="true"><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mroot><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mroot><mo>)</mo></mrow><mrow><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mroot><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mroot><mi>x</mi><mo>+</mo><mroot><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mroot><mo>)</mo></mrow></mstyle></math> by multiplying each term in the first expression by each term in the second expression.

Simplify terms.

Simplify each term.

Multiply <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by adding the exponents.

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

Raise <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Rewrite using the commutative property of multiplication.

Multiply <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by adding the exponents.

Move <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mroot><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mroot><mrow><mo>(</mo><mroot><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mroot><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mroot><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mroot></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mroot><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mroot></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msup><mrow><mroot><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mroot></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msup></mstyle></math> .

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

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mroot><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mroot><mroot><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mroot></mstyle></math> .

Combine using the product rule for radicals.

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical, assuming real numbers.

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

Combine the opposite terms in <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>+</mo><mroot><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mroot><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>x</mi><mroot><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mroot><mo>-</mo><mroot><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mroot><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mroot><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mroot><mi>x</mi><mo>-</mo><mn>2</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mroot><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mroot><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> from <math><mstyle displaystyle="true"><mroot><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mroot><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Add <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>+</mo><mi>x</mi><mroot><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mroot></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Reorder the factors in the terms <math><mstyle displaystyle="true"><mi>x</mi><mroot><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mroot></mstyle></math> and <math><mstyle displaystyle="true"><mo>-</mo><mroot><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mroot><mi>x</mi></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mi>x</mi><mroot><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mroot></mstyle></math> from <math><mstyle displaystyle="true"><mi>x</mi><mroot><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mroot></mstyle></math> .

Add <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Since the two sides have been shown to be equivalent, the equation is an identity.

Do you know how to Verify the Identity x^3-2=(x- cube root of 2)(x^2+ cube root of 2x+ cube root of 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 sixty-nine million two hundred seventy-nine thousand two hundred fifty-two |
---|

- 869279252 has 32 divisors, whose sum is
**1981923552** - The reverse of 869279252 is
**252972968** - Previous prime number is
**1907**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 50
- Digital Root 5

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

- 1593045838 has 8 divisors, whose sum is
**2390623200** - The reverse of 1593045838 is
**8385403951** - Previous prime number is
**2281**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 46
- Digital Root 1

Name | seven hundred eighty-seven million two hundred eighty thousand twenty-six |
---|

- 787280026 has 8 divisors, whose sum is
**1271760084** - The reverse of 787280026 is
**620082787** - Previous prime number is
**13**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 40
- Digital Root 4