Algebra Examples

${(v - \frac{1}{5} s)}^{2}$

Step 1

Combine fractions.

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Step 1.1

Combine $s$ and $\frac{1}{5}$ .

${(v - \frac{s}{5})}^{2}$

Step 1.2

Rewrite ${(v - \frac{s}{5})}^{2}$ as $(v - \frac{s}{5}) (v - \frac{s}{5})$ .

$(v - \frac{s}{5}) (v - \frac{s}{5})$

Step 2

Expand $(v - \frac{s}{5}) (v - \frac{s}{5})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$v (v - \frac{s}{5}) - \frac{s}{5} (v - \frac{s}{5})$

Step 2.2

Apply the distributive property.

$v \cdot v + v (- \frac{s}{5}) - \frac{s}{5} (v - \frac{s}{5})$

Step 2.3

Apply the distributive property.

$v \cdot v + v (- \frac{s}{5}) - \frac{s}{5} v - \frac{s}{5} (- \frac{s}{5})$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $v$ by $v$ .

$v^{2} + v (- \frac{s}{5}) - \frac{s}{5} v - \frac{s}{5} (- \frac{s}{5})$

Step 3.1.2

Rewrite using the commutative property of multiplication.

$v^{2} - v \frac{s}{5} - \frac{s}{5} v - \frac{s}{5} (- \frac{s}{5})$

Step 3.1.3

Combine $\frac{s}{5}$ and $v$ .

$v^{2} - \frac{s v}{5} - \frac{s}{5} v - \frac{s}{5} (- \frac{s}{5})$

Step 3.1.4

Combine $v$ and $\frac{s}{5}$ .

$v^{2} - \frac{s v}{5} - \frac{v s}{5} - \frac{s}{5} (- \frac{s}{5})$

Step 3.1.5

Multiply $- \frac{s}{5} (- \frac{s}{5})$ .

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Step 3.1.5.1

Multiply $- 1$ by $- 1$ .

$v^{2} - \frac{s v}{5} - \frac{v s}{5} + 1 \frac{s}{5} \frac{s}{5}$

Step 3.1.5.2

Multiply $\frac{s}{5}$ by $1$ .

$v^{2} - \frac{s v}{5} - \frac{v s}{5} + \frac{s}{5} \cdot \frac{s}{5}$

Step 3.1.5.3

Multiply $\frac{s}{5}$ by $\frac{s}{5}$ .

$v^{2} - \frac{s v}{5} - \frac{v s}{5} + \frac{s \cdot s}{5 \cdot 5}$

Step 3.1.5.4

Raise $s$ to the power of $1$ .

$v^{2} - \frac{s v}{5} - \frac{v s}{5} + \frac{s^{1} s}{5 \cdot 5}$

Step 3.1.5.5

Raise $s$ to the power of $1$ .

$v^{2} - \frac{s v}{5} - \frac{v s}{5} + \frac{s^{1} s^{1}}{5 \cdot 5}$

Step 3.1.5.6

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

$v^{2} - \frac{s v}{5} - \frac{v s}{5} + \frac{s^{1 + 1}}{5 \cdot 5}$

Step 3.1.5.7

Add $1$ and $1$ .

$v^{2} - \frac{s v}{5} - \frac{v s}{5} + \frac{s^{2}}{5 \cdot 5}$

Step 3.1.5.8

Multiply $5$ by $5$ .

$v^{2} - \frac{s v}{5} - \frac{v s}{5} + \frac{s^{2}}{25}$

Step 3.2

Subtract $\frac{v s}{5}$ from $- \frac{s v}{5}$ .

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Step 3.2.1

Reorder $v$ and $s$ .

$v^{2} - \frac{s v}{5} - \frac{s v}{5} + \frac{s^{2}}{25}$

Step 3.2.2

Subtract $\frac{s v}{5}$ from $- \frac{s v}{5}$ .

$v^{2} - 2 \frac{s v}{5} + \frac{s^{2}}{25}$

Step 4

Simplify each term.

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Step 4.1

Combine $- 2$ and $\frac{s v}{5}$ .

$v^{2} + \frac{- 2 (s v)}{5} + \frac{s^{2}}{25}$

Step 4.2

Move the negative in front of the fraction.

$v^{2} - \frac{2 s v}{5} + \frac{s^{2}}{25}$

Step 5

Simplify the expression.

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Step 5.1

Move $v^{2}$ .

$- \frac{2 s v}{5} + \frac{s^{2}}{25} + v^{2}$

Step 5.2

Reorder $- \frac{2 s v}{5}$ and $\frac{s^{2}}{25}$ .

$\frac{s^{2}}{25} - \frac{2 s v}{5} + v^{2}$