Algebra Examples

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify terms.

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Step 3.1

Combine the opposite terms in $x^{2} x^{2} + x^{2} (2 y) - 2 y x^{2} - 2 y (2 y)$ .

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Step 3.1.1

Reorder the factors in the terms $x^{2} (2 y)$ and $- 2 y x^{2}$ .

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

Step 3.1.2

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

$x^{2} x^{2} + 0 - 2 y (2 y)$

Step 3.1.3

Add $x^{2} x^{2}$ and $0$ .

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

Step 3.2

Simplify each term.

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Step 3.2.1

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

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Step 3.2.1.1

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

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

Step 3.2.1.2

Add $2$ and $2$ .

$x^{4} - 2 y (2 y)$

Step 3.2.2

Rewrite using the commutative property of multiplication.

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

Step 3.2.3

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

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Step 3.2.3.1

Move $y$ .

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

Step 3.2.3.2

Multiply $y$ by $y$ .

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

Step 3.2.4

Multiply $- 2$ by $2$ .

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