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

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

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=-b\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$a^{3}-ab^{2}=a^{3}+b^{3}$$

Subtract a^{3} from both sides.

$$a^{3}-ab^{2}-a^{3}=b^{3}$$

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

$$-ab^{2}=b^{3}$$

The equation is in standard form.

$$\left(-b^{2}\right)a=b^{3}$$

Divide both sides by -b^{2}.

$$\frac{\left(-b^{2}\right)a}{-b^{2}}=\frac{b^{3}}{-b^{2}}$$

Dividing by -b^{2} undoes the multiplication by -b^{2}.

$$a=\frac{b^{3}}{-b^{2}}$$

Divide b^{3} by -b^{2}.

$$a=-b$$

Solve for a

$$\left\{\begin{matrix}\\a=-b\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$a^{3}-ab^{2}=a^{3}+b^{3}$$

Subtract a^{3} from both sides.

$$a^{3}-ab^{2}-a^{3}=b^{3}$$

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

$$-ab^{2}=b^{3}$$

The equation is in standard form.

$$\left(-b^{2}\right)a=b^{3}$$

Divide both sides by -b^{2}.

$$\frac{\left(-b^{2}\right)a}{-b^{2}}=\frac{b^{3}}{-b^{2}}$$

Dividing by -b^{2} undoes the multiplication by -b^{2}.

$$a=\frac{b^{3}}{-b^{2}}$$

Divide b^{3} by -b^{2}.

$$a=-b$$

Solve for b

$$b=0$$

$$b=-a$$