Basic Math Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.1.3

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

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

Step 2.2

Simplify each term.

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Step 2.2.1

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

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Step 2.2.1.1

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

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

Step 2.2.1.2

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

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

Step 2.2.1.3

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

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

Step 2.2.1.4

Add $1$ and $1$ .

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

Step 2.2.2

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

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Step 2.2.2.1

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

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

Step 2.2.2.2

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

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

Step 2.2.2.3

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

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

Step 2.2.2.4

Cancel the common factor of $2$ .

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Step 2.2.2.4.1

Cancel the common factor.

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

Step 2.2.2.4.2

Rewrite the expression.

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

Step 2.2.2.5

Simplify.

$y - x \cdot x$

Step 2.2.3

Multiply $x$ by $x$ by adding the exponents.

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Step 2.2.3.1

Move $x$ .

$y - (x \cdot x)$

Step 2.2.3.2

Multiply $x$ by $x$ .

$y - x^{2}$