Algebra Examples

$1 - 2.25 x^{8}$

Step 1

Rewrite $1$ as $1^{2}$ .

$1^{2} - 2.25 x^{8}$

Step 2

Rewrite $2.25 x^{8}$ as ${(1.5 x^{4})}^{2}$ .

$1^{2} - {(1.5 x^{4})}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = 1.5 x^{4}$ .

$(1 + 1.5 x^{4}) (1 - (1.5 x^{4}))$

Step 4

Simplify.

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Step 4.1

Remove parentheses.

$(1 + 1.5 x^{4}) (1 - 1 \cdot 1.5 x^{4})$

Step 4.2

Rewrite $1$ as $1^{2}$ .

$(1 + 1.5 x^{4}) (1^{2} - 1 \cdot 1.5 x^{4})$

Step 4.3

Rewrite $1.5 x^{4}$ as ${(1.22474487 x^{2})}^{2}$ .

$(1 + 1.5 x^{4}) (1^{2} - {(1.22474487 x^{2})}^{2})$

Step 4.4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = 1.22474487 x^{2}$ .

$(1 + 1.5 x^{4}) ((1 + 1.22474487 x^{2}) (1 - (1.22474487 x^{2})))$

Step 4.5

Factor.

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Step 4.5.1

Simplify.

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Step 4.5.1.1

Remove parentheses.

$(1 + 1.5 x^{4}) ((1 + 1.22474487 x^{2}) (1 - 1 \cdot 1.22474487 x^{2}))$

Step 4.5.1.2

Rewrite $1$ as $1^{2}$ .

$(1 + 1.5 x^{4}) ((1 + 1.22474487 x^{2}) (1^{2} - 1 \cdot 1.22474487 x^{2}))$

Step 4.5.1.3

Rewrite $1.22474487 x^{2}$ as ${(1.10668191 x)}^{2}$ .

$(1 + 1.5 x^{4}) ((1 + 1.22474487 x^{2}) (1^{2} - {(1.10668191 x)}^{2}))$

Step 4.5.1.4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = 1.10668191 x$ .

$(1 + 1.5 x^{4}) ((1 + 1.22474487 x^{2}) ((1 + 1.10668191 x) (1 - (1.10668191 x))))$

Step 4.5.1.5

Factor.

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Step 4.5.1.5.1

Multiply $1.10668191$ by $- 1$ .

$(1 + 1.5 x^{4}) ((1 + 1.22474487 x^{2}) ((1 + 1.10668191 x) (1 - 1.10668191 x)))$

Step 4.5.1.5.2

Remove unnecessary parentheses.

$(1 + 1.5 x^{4}) ((1 + 1.22474487 x^{2}) (1 + 1.10668191 x) (1 - 1.10668191 x))$

Step 4.5.2

Remove unnecessary parentheses.

$(1 + 1.5 x^{4}) (1 + 1.22474487 x^{2}) (1 + 1.10668191 x) (1 - 1.10668191 x)$