Algebra Examples

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

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

Step 1

Expand

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

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

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Step 1.1

Apply the distributive property.

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

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

Step 1.2

Apply the distributive property.

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

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

Step 1.3

Apply the distributive property.

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

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

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

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in

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

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

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Step 2.1.1

Reorder the factors in the terms

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

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

y^{2} x^{2}

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

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

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

Step 2.1.2

Add

- x^{2} y^{2}

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

x^{2} y^{2}

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

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

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

Step 2.1.3

Add

x^{2} x^{2}

$x^{2} x^{2}$ and

0

$0$ .

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

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

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

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

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply

x^{2}

$x^{2}$ by

x^{2}

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

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Step 2.2.1.1

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 2.2.1.2

Add

2

$2$ and

2

$2$ .

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

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

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

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

Step 2.2.2

Rewrite using the commutative property of multiplication.

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

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

Step 2.2.3

Multiply

y^{2}

$y^{2}$ by

y^{2}

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

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Step 2.2.3.1

Move

y^{2}

$y^{2}$ .

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

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

Step 2.2.3.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 2.2.3.3

Add

2

$2$ and

2

$2$ .

x^{4} - y^{4}

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

x^{4} - y^{4}

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

x^{4} - y^{4}

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

x^{4} - y^{4}

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