Algebra Examples

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

Step 1

Expand $(x^{2} + 4 y^{2}) (x^{2} - 4 y^{2})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $x^{2} x^{2} + x^{2} (- 4 y^{2}) + 4 y^{2} x^{2} + 4 y^{2} (- 4 y^{2})$ .

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Step 2.1.1

Reorder the factors in the terms $x^{2} (- 4 y^{2})$ and $4 y^{2} x^{2}$ .

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

Step 2.1.2

Add $- 4 x^{2} y^{2}$ and $4 x^{2} y^{2}$ .

$x^{2} x^{2} + 0 + 4 y^{2} (- 4 y^{2})$

Step 2.1.3

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

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

Step 2.2

Simplify each term.

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Step 2.2.1

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

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Step 2.2.1.1

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

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

Step 2.2.1.2

Add $2$ and $2$ .

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

Step 2.2.2

Rewrite using the commutative property of multiplication.

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

Step 2.2.3

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

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Step 2.2.3.1

Move $y^{2}$ .

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

Step 2.2.3.2

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

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

Step 2.2.3.3

Add $2$ and $2$ .

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

Step 2.2.4

Multiply $4$ by $- 4$ .

$x^{4} - 16 y^{4}$