Algebra Examples

$x^{2} + {(\frac{1}{x})}^{2} + 2$

Step 1

Rearrange terms.

$x^{2} + 2 + {(\frac{1}{x})}^{2}$

Step 2

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

$2 = 2 \cdot x \cdot \frac{1}{x}$

Step 3

Rewrite the polynomial.

$x^{2} + 2 \cdot x \cdot \frac{1}{x} + {(\frac{1}{x})}^{2}$

Step 4

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

${(x + \frac{1}{x})}^{2}$