Basic Math Examples

$(p + p^{\frac{1}{2}}) (p - p^{\frac{1}{2}})$

Step 1

Expand $(p + p^{\frac{1}{2}}) (p - p^{\frac{1}{2}})$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$p (p - p^{\frac{1}{2}}) + p^{\frac{1}{2}} (p - p^{\frac{1}{2}})$

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Combine the opposite terms in $p \cdot p + p (- p^{\frac{1}{2}}) + p^{\frac{1}{2}} p + p^{\frac{1}{2}} (- p^{\frac{1}{2}})$ .

Tap for more steps...

Step 2.1.1

Reorder the factors in the terms $p (- p^{\frac{1}{2}})$ and $p^{\frac{1}{2}} p$ .

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

Step 2.1.2

Add $- p^{\frac{1}{2}} p$ and $p^{\frac{1}{2}} p$ .

$p \cdot p + 0 + p^{\frac{1}{2}} (- p^{\frac{1}{2}})$

Step 2.1.3

Add $p \cdot p$ and $0$ .

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

Step 2.2

Simplify each term.

Tap for more steps...

Step 2.2.1

Multiply $p$ by $p$ .

$p^{2} + p^{\frac{1}{2}} (- p^{\frac{1}{2}})$

Step 2.2.2

Rewrite using the commutative property of multiplication.

$p^{2} - p^{\frac{1}{2}} p^{\frac{1}{2}}$

Step 2.2.3

Multiply $p^{\frac{1}{2}}$ by $p^{\frac{1}{2}}$ by adding the exponents.

Tap for more steps...

Step 2.2.3.1

Move $p^{\frac{1}{2}}$ .

$p^{2} - (p^{\frac{1}{2}} p^{\frac{1}{2}})$

Step 2.2.3.2

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

$p^{2} - p^{\frac{1}{2} + \frac{1}{2}}$

Step 2.2.3.3

Combine the numerators over the common denominator.

$p^{2} - p^{\frac{1 + 1}{2}}$

Step 2.2.3.4

Add $1$ and $1$ .

$p^{2} - p^{\frac{2}{2}}$

Step 2.2.3.5

Divide $2$ by $2$ .

$p^{2} - p^{1}$

Step 2.2.4

Simplify $- p^{1}$ .

$p^{2} - p$