Expand <math><mstyle displaystyle="true"><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>-</mo><mi>c</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>)</mo></mrow></mstyle></math> by multiplying each term in the first expression by each term in the second expression.

Combine the opposite terms in <math><mstyle displaystyle="true"><mi>a</mi><mo>⋅</mo><mi>a</mi><mo>+</mo><mi>a</mi><mi>b</mi><mo>+</mo><mi>a</mi><mi>c</mi><mo>+</mo><mi>b</mi><mi>a</mi><mo>+</mo><mi>b</mi><mo>⋅</mo><mi>b</mi><mo>+</mo><mi>b</mi><mi>c</mi><mo>-</mo><mi>c</mi><mi>a</mi><mo>-</mo><mi>c</mi><mi>b</mi><mo>-</mo><mi>c</mi><mo>⋅</mo><mi>c</mi></mstyle></math> .

Reorder the factors in the terms <math><mstyle displaystyle="true"><mi>a</mi><mi>c</mi></mstyle></math> and <math><mstyle displaystyle="true"><mo>-</mo><mi>c</mi><mi>a</mi></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mi>a</mi><mi>c</mi></mstyle></math> from <math><mstyle displaystyle="true"><mi>a</mi><mi>c</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mi>a</mi><mo>⋅</mo><mi>a</mi><mo>+</mo><mi>a</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>a</mi><mo>+</mo><mi>b</mi><mo>⋅</mo><mi>b</mi><mo>+</mo><mi>b</mi><mi>c</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Reorder the factors in the terms <math><mstyle displaystyle="true"><mi>b</mi><mi>c</mi></mstyle></math> and <math><mstyle displaystyle="true"><mo>-</mo><mi>c</mi><mi>b</mi></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mi>b</mi><mi>c</mi></mstyle></math> from <math><mstyle displaystyle="true"><mi>b</mi><mi>c</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mi>a</mi><mo>⋅</mo><mi>a</mi><mo>+</mo><mi>a</mi><mi>b</mi><mo>+</mo><mi>b</mi><mi>a</mi><mo>+</mo><mi>b</mi><mo>⋅</mo><mi>b</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Simplify each term.

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

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

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

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

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

Reorder <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mi>a</mi><mi>b</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>a</mi><mi>b</mi></mstyle></math> .

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