Simplify ( square root of x- square root of y)( square root of x+ square root of y)

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

Step 1

Expand $(\sqrt{x} - \sqrt{y}) (\sqrt{x} + \sqrt{y})$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$\sqrt{x} \sqrt{x} + \sqrt{x} \sqrt{y} - \sqrt{y} \sqrt{x} - \sqrt{y} \sqrt{y}$

Step 2

Simplify terms.

Combine the opposite terms in $\sqrt{x} \sqrt{x} + \sqrt{x} \sqrt{y} - \sqrt{y} \sqrt{x} - \sqrt{y} \sqrt{y}$ .

Reorder the factors in the terms $\sqrt{x} \sqrt{y}$ and $- \sqrt{y} \sqrt{x}$ .

$\sqrt{x} \sqrt{x} + \sqrt{x} \sqrt{y} - \sqrt{x} \sqrt{y} - \sqrt{y} \sqrt{y}$

Subtract $\sqrt{x} \sqrt{y}$ from $\sqrt{x} \sqrt{y}$ .

$\sqrt{x} \sqrt{x} + 0 - \sqrt{y} \sqrt{y}$

Add $\sqrt{x} \sqrt{x}$ and $0$ .

$\sqrt{x} \sqrt{x} - \sqrt{y} \sqrt{y}$

Simplify each term.

Multiply $\sqrt{x} \sqrt{x}$ .

Raise $\sqrt{x}$ to the power of $1$ .

${\sqrt{x}}^{1} \sqrt{x} - \sqrt{y} \sqrt{y}$

Raise $\sqrt{x}$ to the power of $1$ .

${\sqrt{x}}^{1} {\sqrt{x}}^{1} - \sqrt{y} \sqrt{y}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\sqrt{x}}^{1 + 1} - \sqrt{y} \sqrt{y}$

Add $1$ and $1$ .

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

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

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

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{2} \cdot 2} - \sqrt{y} \sqrt{y}$

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$x^{1} - \sqrt{y} \sqrt{y}$

Simplify.

$x - \sqrt{y} \sqrt{y}$

Multiply $- \sqrt{y} \sqrt{y}$ .

Raise $\sqrt{y}$ to the power of $1$ .

$x - ({\sqrt{y}}^{1} \sqrt{y})$

Raise $\sqrt{y}$ to the power of $1$ .

$x - ({\sqrt{y}}^{1} {\sqrt{y}}^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x - {\sqrt{y}}^{1 + 1}$

Add $1$ and $1$ .

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

Rewrite ${\sqrt{y}}^{2}$ as $y$ .

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

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x - y^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$x - y^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x - y^{\frac{2}{2}}$

Rewrite the expression.

$x - y^{1}$

Simplify.

$x - y$

Simplify ( square root of x- square root of y)( square root of x+ square root of y)

Related Questions

Support LCMGCF.com by disabling your adblocker.