Basic Math Examples

$v^{2} - 2 v + 1 - 9 t^{2}$

Step 1

Factor using the perfect square rule.

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Step 1.1

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

$v^{2} - 2 v + 1^{2} - 9 t^{2}$

Step 1.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 v = 2 \cdot v \cdot 1$

Step 1.3

Rewrite the polynomial.

$v^{2} - 2 \cdot v \cdot 1 + 1^{2} - 9 t^{2}$

Step 1.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = v$ and $b = 1$ .

${(v - 1)}^{2} - 9 t^{2}$

Step 2

Rewrite $9 t^{2}$ as ${(3 t)}^{2}$ .

${(v - 1)}^{2} - {(3 t)}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = v - 1$ and $b = 3 t$ .

$(v - 1 + 3 t) (v - 1 - (3 t))$

Step 4

Multiply $3$ by $- 1$ .

$(v - 1 + 3 t) (v - 1 - 3 t)$