Finite Math Examples

$s^{2} + 2 s t + t^{2} - z^{2}$

Step 1

Factor using the perfect square rule.

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Step 1.1

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

$2 s t = 2 \cdot s \cdot t$

Step 1.2

Rewrite the polynomial.

$s^{2} + 2 \cdot s \cdot t + t^{2} - z^{2}$

Step 1.3

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

${(s + t)}^{2} - z^{2}$

Step 2

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

$(s + t + z) (s + t - z)$