Solve x ^ 3 + y ^ 3 = (x + y)(x ^ 2 - xy + y ^ 2) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$x^{3}+y^{3}=(x+y)(x^{2}-xy+y^{2})$$

Solve for x (complex solution)

$x\in \mathrm{C}$

Solution Steps

Use the distributive property to multiply $x+y$ by $x^{2}-xy+y^{2}$ and combine like terms.

$$x^{3}+y^{3}=x^{3}+y^{3}$$

Subtract $x^{3}$ from both sides.

$$x^{3}+y^{3}-x^{3}=y^{3}$$

Combine $x^{3}$ and $-x^{3}$ to get $0$.

$$y^{3}=y^{3}$$

Reorder the terms.

$$\text{true}$$

This is true for any $x$.

$$x\in \mathrm{C}$$

Solve for y (complex solution)

$y\in \mathrm{C}$

Solution Steps

Use the distributive property to multiply $x+y$ by $x^{2}-xy+y^{2}$ and combine like terms.

$$x^{3}+y^{3}=x^{3}+y^{3}$$

Subtract $y^{3}$ from both sides.

$$x^{3}+y^{3}-y^{3}=x^{3}$$

Combine $y^{3}$ and $-y^{3}$ to get $0$.

$$x^{3}=x^{3}$$

Reorder the terms.

$$\text{true}$$

This is true for any $y$.

$$y\in \mathrm{C}$$

Solve for x

$x\in \mathrm{R}$

Solution Steps

Use the distributive property to multiply $x+y$ by $x^{2}-xy+y^{2}$ and combine like terms.

$$x^{3}+y^{3}=x^{3}+y^{3}$$

Subtract $x^{3}$ from both sides.

$$x^{3}+y^{3}-x^{3}=y^{3}$$

Combine $x^{3}$ and $-x^{3}$ to get $0$.

$$y^{3}=y^{3}$$

Reorder the terms.

$$\text{true}$$

This is true for any $x$.

$$x\in \mathrm{R}$$

Solve for y

$y\in \mathrm{R}$

Solution Steps

Use the distributive property to multiply $x+y$ by $x^{2}-xy+y^{2}$ and combine like terms.

$$x^{3}+y^{3}=x^{3}+y^{3}$$

Subtract $y^{3}$ from both sides.

$$x^{3}+y^{3}-y^{3}=x^{3}$$

Combine $y^{3}$ and $-y^{3}$ to get $0$.

$$x^{3}=x^{3}$$

Reorder the terms.

$$\text{true}$$

This is true for any $y$.

$$y\in \mathrm{R}$$