Precalculus Examples

$(3 \sqrt{x} - 6 \sqrt{y}) (3 \sqrt{x} + 6 \sqrt{y})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$(3 x^{\frac{1}{2}} - 6 \sqrt{y}) (3 \sqrt{x} + 6 \sqrt{y})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y}$ as $y^{\frac{1}{2}}$ .

$(3 x^{\frac{1}{2}} - 6 y^{\frac{1}{2}}) (3 \sqrt{x} + 6 \sqrt{y})$

Step 3

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$(3 x^{\frac{1}{2}} - 6 y^{\frac{1}{2}}) (3 x^{\frac{1}{2}} + 6 \sqrt{y})$

Step 4

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y}$ as $y^{\frac{1}{2}}$ .

$(3 x^{\frac{1}{2}} - 6 y^{\frac{1}{2}}) (3 x^{\frac{1}{2}} + 6 y^{\frac{1}{2}})$