Algebra Examples

$1 - 9 a^{2} b^{4} c^{6} d^{8}$

Step 1

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

$1^{2} - 9 a^{2} b^{4} c^{6} d^{8}$

Step 2

Rewrite $9 a^{2} b^{4} c^{6} d^{8}$ as ${(3 a b^{2} c^{3} d^{4})}^{2}$ .

$1^{2} - {(3 a b^{2} c^{3} d^{4})}^{2}$

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 $b = 3 a b^{2} c^{3} d^{4}$ .

$(1 + 3 a b^{2} c^{3} d^{4}) (1 - (3 a b^{2} c^{3} d^{4}))$

Step 4

Simplify.

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Step 4.1

Multiply $3$ by $- 1$ .

$(1 + 3 a b^{2} c^{3} d^{4}) (1 - 3 (a b^{2} c^{3} d^{4}))$

Step 4.2

Remove parentheses.

$(1 + 3 a b^{2} c^{3} d^{4}) (1 - 3 (a b^{2} c^{3}) d^{4})$

Step 4.3

Remove parentheses.

$(1 + 3 a b^{2} c^{3} d^{4}) (1 - 3 (a b^{2}) c^{3} d^{4})$

Step 4.4

Remove parentheses.

$(1 + 3 a b^{2} c^{3} d^{4}) (1 - 3 a b^{2} c^{3} d^{4})$