Basic Math Examples

1 - a^{4}

$1 - a^{4}$

Step 1

Rewrite

1

$1$ as

1^{2}

$1^{2}$ .

1^{2} - a^{4}

$1^{2} - a^{4}$

Step 2

Rewrite

a^{4}

$a^{4}$ as

{(a^{2})}^{2}

${(a^{2})}^{2}$ .

1^{2} - {(a^{2})}^{2}

$1^{2} - {(a^{2})}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ where

a = 1

$a = 1$ and

b = a^{2}

$b = a^{2}$ .

(1 + a^{2}) (1 - a^{2})

$(1 + a^{2}) (1 - a^{2})$

Step 4

Simplify.

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Step 4.1

Rewrite

1

$1$ as

1^{2}

$1^{2}$ .

(1 + a^{2}) (1^{2} - a^{2})

$(1 + a^{2}) (1^{2} - a^{2})$

Step 4.2

Factor.

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Step 4.2.1

Since both terms are perfect squares, factor using the difference of squares formula,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ where

a = 1

$a = 1$ and

b = a

$b = a$ .

(1 + a^{2}) ((1 + a) (1 - a))

$(1 + a^{2}) ((1 + a) (1 - a))$

Step 4.2.2

Remove unnecessary parentheses.

(1 + a^{2}) (1 + a) (1 - a)

$(1 + a^{2}) (1 + a) (1 - a)$

(1 + a^{2}) (1 + a) (1 - a)

$(1 + a^{2}) (1 + a) (1 - a)$

(1 + a^{2}) (1 + a) (1 - a)

$(1 + a^{2}) (1 + a) (1 - a)$