Solve (a+b)(a^2-ab+b^2)=a^3+b^3

$$( a + b ) ( a ^ { 2 } - a b + b ^ { 2 } ) = a ^ { 3 } + b ^ { 3 }$$

Solve for a (complex solution)

$$a\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply a+b by a^{2}-ab+b^{2} and combine like terms.

$$a^{3}+b^{3}=a^{3}+b^{3}$$

Subtract a^{3} from both sides.

$$a^{3}+b^{3}-a^{3}=b^{3}$$

Combine a^{3} and -a^{3} to get 0.

$$b^{3}=b^{3}$$

Reorder the terms.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{C}$$

Solve for b (complex solution)

$$b\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply a+b by a^{2}-ab+b^{2} and combine like terms.

$$a^{3}+b^{3}=a^{3}+b^{3}$$

Subtract b^{3} from both sides.

$$a^{3}+b^{3}-b^{3}=a^{3}$$

Combine b^{3} and -b^{3} to get 0.

$$a^{3}=a^{3}$$

Reorder the terms.

$$\text{true}$$

This is true for any b.

$$b\in \mathrm{C}$$

Solve for a

$$a\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply a+b by a^{2}-ab+b^{2} and combine like terms.

$$a^{3}+b^{3}=a^{3}+b^{3}$$

Subtract a^{3} from both sides.

$$a^{3}+b^{3}-a^{3}=b^{3}$$

Combine a^{3} and -a^{3} to get 0.

$$b^{3}=b^{3}$$

Reorder the terms.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{R}$$

Solve for b

$$b\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply a+b by a^{2}-ab+b^{2} and combine like terms.

$$a^{3}+b^{3}=a^{3}+b^{3}$$

Subtract b^{3} from both sides.

$$a^{3}+b^{3}-b^{3}=a^{3}$$

Combine b^{3} and -b^{3} to get 0.

$$a^{3}=a^{3}$$

Reorder the terms.

$$\text{true}$$

This is true for any b.

$$b\in \mathrm{R}$$