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

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

Solve for a (complex solution)

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

Solution Steps

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

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

Cancel out -1 on both sides.

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

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}+b^{2}+ab and combine like terms.

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

Add b^{3} to 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}+b^{2}+ab 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.

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

Cancel out -1 on both sides.

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

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}+b^{2}+ab and combine like terms.

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

Add b^{3} to 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.

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