Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Move $x^{2}$ .

$2 (x^{2} x^{2}) + 2 x^{2} y - y x^{2} - y \cdot y$

Step 2.1.1.2

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

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

Step 2.1.1.3

Add $2$ and $2$ .

$2 x^{4} + 2 x^{2} y - y x^{2} - y \cdot y$

Step 2.1.2

Multiply $y$ by $y$ by adding the exponents.

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Step 2.1.2.1

Move $y$ .

$2 x^{4} + 2 x^{2} y - y x^{2} - (y \cdot y)$

Step 2.1.2.2

Multiply $y$ by $y$ .

$2 x^{4} + 2 x^{2} y - y x^{2} - y^{2}$

Step 2.2

Subtract $y x^{2}$ from $2 x^{2} y$ .

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Step 2.2.1

Move $y$ .

$2 x^{4} + 2 x^{2} y - 1 x^{2} y - y^{2}$

Step 2.2.2

Subtract $x^{2} y$ from $2 x^{2} y$ .

$2 x^{4} + 1 x^{2} y - y^{2}$

Step 3

Multiply $x^{2}$ by $1$ .

$2 x^{4} + x^{2} y - y^{2}$