Algebra Examples

$y^{2} - \sqrt{8 y} = \sqrt{18 y} - 1$

Step 1

Rewrite $y^{2} - \sqrt{8 y}$ as a difference of squares.

$y^{2} - {\sqrt{2 \sqrt{2 y}}}^{2}$

Step 2

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

$(y + \sqrt{2 \sqrt{2 y}}) (y - \sqrt{2 \sqrt{2 y}})$