Algebra Examples

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

Step 1

Expand $(x^{2} + y) (x + y^{2})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

$x^{2} x + x^{2} y^{2} + y x + y \cdot y^{2}$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 2.1.1.1

Multiply $x^{2}$ by $x$ .

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Step 2.1.1.1.1

Raise $x$ to the power of $1$ .

$x^{2} x^{1} + x^{2} y^{2} + y x + y \cdot y^{2}$

Step 2.1.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2 + 1} + x^{2} y^{2} + y x + y \cdot y^{2}$

Step 2.1.1.2

Add $2$ and $1$ .

$x^{3} + x^{2} y^{2} + y x + y \cdot y^{2}$

Step 2.1.2

Multiply $y$ by $y^{2}$ by adding the exponents.

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Step 2.1.2.1

Multiply $y$ by $y^{2}$ .

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Step 2.1.2.1.1

Raise $y$ to the power of $1$ .

$x^{3} + x^{2} y^{2} + y x + y^{1} y^{2}$

Step 2.1.2.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{3} + x^{2} y^{2} + y x + y^{1 + 2}$

Step 2.1.2.2

Add $1$ and $2$ .

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

Step 2.2

Simplify the expression.

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Step 2.2.1

Reorder $y$ and $x$ .

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

Step 2.2.2

Move $x y$ .

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

Step 2.2.3

Reorder $x^{3}$ and $x^{2} y^{2}$ .

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