Simplify (3m^3-1/2y)(3m^3-1/2y)

$(3 m^{3} - \frac{1}{2} y) (3 m^{3} - \frac{1}{2} y)$

Step 1

Combine fractions.

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

$(3 m^{3} - \frac{y}{2}) (3 m^{3} - \frac{1}{2} y)$

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

$(3 m^{3} - \frac{y}{2}) (3 m^{3} - \frac{y}{2})$

Step 2

Expand $(3 m^{3} - \frac{y}{2}) (3 m^{3} - \frac{y}{2})$ using the FOIL Method.

Apply the distributive property.

$3 m^{3} (3 m^{3} - \frac{y}{2}) - \frac{y}{2} (3 m^{3} - \frac{y}{2})$

Apply the distributive property.

$3 m^{3} (3 m^{3}) + 3 m^{3} (- \frac{y}{2}) - \frac{y}{2} (3 m^{3} - \frac{y}{2})$

Apply the distributive property.

$3 m^{3} (3 m^{3}) + 3 m^{3} (- \frac{y}{2}) - \frac{y}{2} (3 m^{3}) - \frac{y}{2} (- \frac{y}{2})$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 m^{3} m^{3} + 3 m^{3} (- \frac{y}{2}) - \frac{y}{2} (3 m^{3}) - \frac{y}{2} (- \frac{y}{2})$

Multiply $m^{3}$ by $m^{3}$ by adding the exponents.

Move $m^{3}$ .

$3 \cdot 3 (m^{3} m^{3}) + 3 m^{3} (- \frac{y}{2}) - \frac{y}{2} (3 m^{3}) - \frac{y}{2} (- \frac{y}{2})$

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

$3 \cdot 3 m^{3 + 3} + 3 m^{3} (- \frac{y}{2}) - \frac{y}{2} (3 m^{3}) - \frac{y}{2} (- \frac{y}{2})$

Add $3$ and $3$ .

$3 \cdot 3 m^{6} + 3 m^{3} (- \frac{y}{2}) - \frac{y}{2} (3 m^{3}) - \frac{y}{2} (- \frac{y}{2})$

Multiply $3$ by $3$ .

$9 m^{6} + 3 m^{3} (- \frac{y}{2}) - \frac{y}{2} (3 m^{3}) - \frac{y}{2} (- \frac{y}{2})$

Multiply $3 m^{3} (- \frac{y}{2})$ .

Multiply $- 1$ by $3$ .

$9 m^{6} - 3 m^{3} \frac{y}{2} - \frac{y}{2} (3 m^{3}) - \frac{y}{2} (- \frac{y}{2})$

Combine $- 3$ and $\frac{y}{2}$ .

$9 m^{6} + m^{3} \frac{- 3 y}{2} - \frac{y}{2} (3 m^{3}) - \frac{y}{2} (- \frac{y}{2})$

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

$9 m^{6} + \frac{m^{3} (- 3 y)}{2} - \frac{y}{2} (3 m^{3}) - \frac{y}{2} (- \frac{y}{2})$

Remove unnecessary parentheses.

$9 m^{6} + \frac{m^{3} \cdot - 3 y}{2} - \frac{y}{2} (3 m^{3}) - \frac{y}{2} (- \frac{y}{2})$

Move $- 3$ to the left of $m^{3}$ .

$9 m^{6} + \frac{- 3 \cdot m^{3} y}{2} - \frac{y}{2} (3 m^{3}) - \frac{y}{2} (- \frac{y}{2})$

Move the negative in front of the fraction.

$9 m^{6} - \frac{(3) \cdot m^{3} y}{2} - \frac{y}{2} (3 m^{3}) - \frac{y}{2} (- \frac{y}{2})$

Multiply $- \frac{y}{2} (3 m^{3})$ .

Multiply $3$ by $- 1$ .

$9 m^{6} - \frac{3 m^{3} y}{2} - 3 \frac{y}{2} m^{3} - \frac{y}{2} (- \frac{y}{2})$

Combine $- 3$ and $\frac{y}{2}$ .

$9 m^{6} - \frac{3 m^{3} y}{2} + \frac{- 3 y}{2} m^{3} - \frac{y}{2} (- \frac{y}{2})$

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

$9 m^{6} - \frac{3 m^{3} y}{2} + \frac{- 3 y m^{3}}{2} - \frac{y}{2} (- \frac{y}{2})$

Move the negative in front of the fraction.

$9 m^{6} - \frac{3 m^{3} y}{2} - \frac{(3) y m^{3}}{2} - \frac{y}{2} (- \frac{y}{2})$

Multiply $- \frac{y}{2} (- \frac{y}{2})$ .

Multiply $- 1$ by $- 1$ .

$9 m^{6} - \frac{3 m^{3} y}{2} - \frac{3 y m^{3}}{2} + 1 \frac{y}{2} \frac{y}{2}$

Multiply $\frac{y}{2}$ by $1$ .

$9 m^{6} - \frac{3 m^{3} y}{2} - \frac{3 y m^{3}}{2} + \frac{y}{2} \cdot \frac{y}{2}$

Multiply $\frac{y}{2}$ by $\frac{y}{2}$ .

$9 m^{6} - \frac{3 m^{3} y}{2} - \frac{3 y m^{3}}{2} + \frac{y \cdot y}{2 \cdot 2}$

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

$9 m^{6} - \frac{3 m^{3} y}{2} - \frac{3 y m^{3}}{2} + \frac{y^{1} y}{2 \cdot 2}$

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

$9 m^{6} - \frac{3 m^{3} y}{2} - \frac{3 y m^{3}}{2} + \frac{y^{1} y^{1}}{2 \cdot 2}$

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

$9 m^{6} - \frac{3 m^{3} y}{2} - \frac{3 y m^{3}}{2} + \frac{y^{1 + 1}}{2 \cdot 2}$

Add $1$ and $1$ .

$9 m^{6} - \frac{3 m^{3} y}{2} - \frac{3 y m^{3}}{2} + \frac{y^{2}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$9 m^{6} - \frac{3 m^{3} y}{2} - \frac{3 y m^{3}}{2} + \frac{y^{2}}{4}$

Subtract $\frac{3 y m^{3}}{2}$ from $- \frac{3 m^{3} y}{2}$ .

Move $y$ .

$9 m^{6} - \frac{3 m^{3} y}{2} - \frac{3 m^{3} y}{2} + \frac{y^{2}}{4}$

Subtract $\frac{3 m^{3} y}{2}$ from $- \frac{3 m^{3} y}{2}$ .

$9 m^{6} - 2 \frac{3 m^{3} y}{2} + \frac{y^{2}}{4}$

Step 4

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$9 m^{6} + 2 (- 1) \frac{3 m^{3} y}{2} + \frac{y^{2}}{4}$

Cancel the common factor.

$9 m^{6} + 2 \cdot - 1 \frac{3 m^{3} y}{2} + \frac{y^{2}}{4}$

Rewrite the expression.

$9 m^{6} - 1 (3 m^{3} y) + \frac{y^{2}}{4}$

Multiply $3$ by $- 1$ .

$9 m^{6} - 3 m^{3} y + \frac{y^{2}}{4}$

Simplify (3m^3-1/2y)(3m^3-1/2y)

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