Solve x(x ^ 2 - xy + y ^ 2) + 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

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

Evaluate

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

Solution Steps

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

$$x^{3}-yx^{2}+xy^{2}+y\left(x^{2}-xy+y^{2}\right)$$

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

$$x^{3}-yx^{2}+xy^{2}+yx^{2}-xy^{2}+y^{3}$$

Combine $-yx^{2}$ and $yx^{2}$ to get $0$.

$$x^{3}+xy^{2}-xy^{2}+y^{3}$$

Combine $xy^{2}$ and $-xy^{2}$ to get $0$.

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

Expand

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

Solution Steps

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

$$x^{3}-yx^{2}+xy^{2}+y\left(x^{2}-xy+y^{2}\right)$$

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

$$x^{3}-yx^{2}+xy^{2}+yx^{2}-xy^{2}+y^{3}$$

Combine $-yx^{2}$ and $yx^{2}$ to get $0$.

$$x^{3}+xy^{2}-xy^{2}+y^{3}$$

Combine $xy^{2}$ and $-xy^{2}$ to get $0$.

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