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 | seventy-two million one hundred seventeen thousand nine hundred ten |
---|

- 72117910 has 16 divisors, whose sum is
**137448576** - The reverse of 72117910 is
**01971127** - Previous prime number is
**17**

- Is Prime? no
- Number parity even
- Number length 8
- Sum of Digits 28
- Digital Root 1

Name | one billion nine hundred sixty-three million one hundred twenty-five thousand one hundred ninety-two |
---|

- 1963125192 has 128 divisors, whose sum is
**10246818816** - The reverse of 1963125192 is
**2915213691** - Previous prime number is
**67**

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

Name | five hundred eighty-four million nine hundred sixty-nine thousand eight hundred seventy-seven |
---|

- 584969877 has 8 divisors, whose sum is
**866622080** - The reverse of 584969877 is
**778969485** - Previous prime number is
**9**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 63
- Digital Root 9