Rewrite <math><mstyle displaystyle="true"><mn>8</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mn>2</mn><mi>x</mi><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></msup></mstyle></math> .

Since both terms are perfect cubes, factor using the difference of cubes formula, <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>-</mo><msup><mrow><mi>b</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>=</mo><mrow><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo></mrow><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>a</mi><mi>b</mi><mo>+</mo><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mstyle></math> where <math><mstyle displaystyle="true"><mi>a</mi><mo>=</mo><mn>2</mn><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mn>1</mn></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mn>2</mn><mi>x</mi></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"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

One to any power is one.

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