Algebra Examples

$(6 v - \frac{3}{4} m w) (6 v + \frac{3}{4} m w)$

Step 1

Simplify terms.

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Step 1.1

Simplify each term.

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Step 1.1.1

Multiply $- \frac{3}{4} (m w)$ .

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Step 1.1.1.1

Combine $m$ and $\frac{3}{4}$ .

$(6 v - \frac{m \cdot 3}{4} w) (6 v + \frac{3}{4} \cdot (m w))$

Step 1.1.1.2

Combine $w$ and $\frac{m \cdot 3}{4}$ .

$(6 v - \frac{w (m \cdot 3)}{4}) (6 v + \frac{3}{4} \cdot (m w))$

Step 1.1.2

Move $3$ to the left of $w m$ .

$(6 v - \frac{3 w m}{4}) (6 v + \frac{3}{4} \cdot (m w))$

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply $\frac{3}{4} (m w)$ .

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Step 1.2.1.1

Combine $m$ and $\frac{3}{4}$ .

$(6 v - \frac{3 w m}{4}) (6 v + \frac{m \cdot 3}{4} w)$

Step 1.2.1.2

Combine $\frac{m \cdot 3}{4}$ and $w$ .

$(6 v - \frac{3 w m}{4}) (6 v + \frac{m \cdot 3 w}{4})$

Step 1.2.2

Move $3$ to the left of $m$ .

$(6 v - \frac{3 w m}{4}) (6 v + \frac{3 m w}{4})$

Step 2

Expand $(6 v - \frac{3 w m}{4}) (6 v + \frac{3 m w}{4})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$6 v (6 v + \frac{3 m w}{4}) - \frac{3 w m}{4} (6 v + \frac{3 m w}{4})$

Step 2.2

Apply the distributive property.

$6 v (6 v) + 6 v \frac{3 m w}{4} - \frac{3 w m}{4} (6 v + \frac{3 m w}{4})$

Step 2.3

Apply the distributive property.

$6 v (6 v) + 6 v \frac{3 m w}{4} - \frac{3 w m}{4} (6 v) - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

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

Rewrite using the commutative property of multiplication.

$6 \cdot 6 v \cdot v + 6 v \frac{3 m w}{4} - \frac{3 w m}{4} (6 v) - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.2

Multiply $v$ by $v$ by adding the exponents.

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Step 3.1.2.1

Move $v$ .

$6 \cdot 6 (v \cdot v) + 6 v \frac{3 m w}{4} - \frac{3 w m}{4} (6 v) - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.2.2

Multiply $v$ by $v$ .

$6 \cdot 6 v^{2} + 6 v \frac{3 m w}{4} - \frac{3 w m}{4} (6 v) - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.3

Multiply $6$ by $6$ .

$36 v^{2} + 6 v \frac{3 m w}{4} - \frac{3 w m}{4} (6 v) - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.4

Cancel the common factor of $2$ .

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Step 3.1.4.1

Factor $2$ out of $6 v$ .

$36 v^{2} + 2 (3 v) \frac{3 m w}{4} - \frac{3 w m}{4} (6 v) - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.4.2

Factor $2$ out of $4$ .

$36 v^{2} + 2 (3 v) \frac{3 m w}{2 (2)} - \frac{3 w m}{4} (6 v) - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.4.3

Cancel the common factor.

$36 v^{2} + 2 (3 v) \frac{3 m w}{2 \cdot 2} - \frac{3 w m}{4} (6 v) - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.4.4

Rewrite the expression.

$36 v^{2} + 3 v \frac{3 m w}{2} - \frac{3 w m}{4} (6 v) - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.5

Combine $3$ and $\frac{3 m w}{2}$ .

$36 v^{2} + v \frac{3 (3 m w)}{2} - \frac{3 w m}{4} (6 v) - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.6

Multiply $3$ by $3$ .

$36 v^{2} + v \frac{9 (m w)}{2} - \frac{3 w m}{4} (6 v) - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.7

Combine $v$ and $\frac{9 (m w)}{2}$ .

$36 v^{2} + \frac{v (9 (m w))}{2} - \frac{3 w m}{4} (6 v) - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.8

Move $9$ to the left of $v$ .

$36 v^{2} + \frac{9 \cdot v m w}{2} - \frac{3 w m}{4} (6 v) - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.9

Cancel the common factor of $2$ .

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Step 3.1.9.1

Move the leading negative in $- \frac{3 w m}{4}$ into the numerator.

$36 v^{2} + \frac{9 v m w}{2} + \frac{- 3 w m}{4} (6 v) - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.9.2

Factor $2$ out of $4$ .

$36 v^{2} + \frac{9 v m w}{2} + \frac{- 3 w m}{2 (2)} (6 v) - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.9.3

Factor $2$ out of $6 v$ .

$36 v^{2} + \frac{9 v m w}{2} + \frac{- 3 w m}{2 (2)} (2 (3 v)) - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.9.4

Cancel the common factor.

$36 v^{2} + \frac{9 v m w}{2} + \frac{- 3 w m}{2 \cdot 2} (2 (3 v)) - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.9.5

Rewrite the expression.

$36 v^{2} + \frac{9 v m w}{2} + \frac{- 3 w m}{2} (3 v) - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.10

Combine $3$ and $\frac{- 3 w m}{2}$ .

$36 v^{2} + \frac{9 v m w}{2} + \frac{3 (- 3 w m)}{2} v - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.11

Multiply $- 3$ by $3$ .

$36 v^{2} + \frac{9 v m w}{2} + \frac{- 9 (w m)}{2} v - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.12

Combine $\frac{- 9 (w m)}{2}$ and $v$ .

$36 v^{2} + \frac{9 v m w}{2} + \frac{- 9 (w m) v}{2} - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.13

Move the negative in front of the fraction.

$36 v^{2} + \frac{9 v m w}{2} - \frac{9 w m v}{2} - \frac{3 w m}{4} \cdot \frac{3 m w}{4}$

Step 3.1.14

Multiply $- \frac{3 w m}{4} \cdot \frac{3 m w}{4}$ .

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Step 3.1.14.1

Multiply $\frac{3 m w}{4}$ by $\frac{3 w m}{4}$ .

$36 v^{2} + \frac{9 v m w}{2} - \frac{9 w m v}{2} - \frac{3 m w (3 w m)}{4 \cdot 4}$

Step 3.1.14.2

Multiply $3$ by $3$ .

$36 v^{2} + \frac{9 v m w}{2} - \frac{9 w m v}{2} - \frac{9 m w (w m)}{4 \cdot 4}$

Step 3.1.14.3

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

$36 v^{2} + \frac{9 v m w}{2} - \frac{9 w m v}{2} - \frac{9 (m^{1} m) w \cdot w}{4 \cdot 4}$

Step 3.1.14.4

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

$36 v^{2} + \frac{9 v m w}{2} - \frac{9 w m v}{2} - \frac{9 (m^{1} m^{1}) w \cdot w}{4 \cdot 4}$

Step 3.1.14.5

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

$36 v^{2} + \frac{9 v m w}{2} - \frac{9 w m v}{2} - \frac{9 m^{1 + 1} w \cdot w}{4 \cdot 4}$

Step 3.1.14.6

Add $1$ and $1$ .

$36 v^{2} + \frac{9 v m w}{2} - \frac{9 w m v}{2} - \frac{9 m^{2} w \cdot w}{4 \cdot 4}$

Step 3.1.14.7

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

$36 v^{2} + \frac{9 v m w}{2} - \frac{9 w m v}{2} - \frac{9 m^{2} (w^{1} w)}{4 \cdot 4}$

Step 3.1.14.8

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

$36 v^{2} + \frac{9 v m w}{2} - \frac{9 w m v}{2} - \frac{9 m^{2} (w^{1} w^{1})}{4 \cdot 4}$

Step 3.1.14.9

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

$36 v^{2} + \frac{9 v m w}{2} - \frac{9 w m v}{2} - \frac{9 m^{2} w^{1 + 1}}{4 \cdot 4}$

Step 3.1.14.10

Add $1$ and $1$ .

$36 v^{2} + \frac{9 v m w}{2} - \frac{9 w m v}{2} - \frac{9 m^{2} w^{2}}{4 \cdot 4}$

Step 3.1.14.11

Multiply $4$ by $4$ .

$36 v^{2} + \frac{9 v m w}{2} - \frac{9 w m v}{2} - \frac{9 m^{2} w^{2}}{16}$

Step 3.2

Move $w$ .

$36 v^{2} + \frac{9 m v w}{2} - \frac{9 m v w}{2} - \frac{9 m^{2} w^{2}}{16}$

Step 3.3

Subtract $\frac{9 m v w}{2}$ from $\frac{9 m v w}{2}$ .

$36 v^{2} + 0 - \frac{9 m^{2} w^{2}}{16}$

Step 3.4

Add $36 v^{2}$ and $0$ .

$36 v^{2} - \frac{9 m^{2} w^{2}}{16}$