Simplify (4m- square root of 3)(4m- square root of 3)

$(4 m - \sqrt{3}) (4 m - \sqrt{3})$

Expand $(4 m - \sqrt{3}) (4 m - \sqrt{3})$ using the FOIL Method.

Apply the distributive property.

$4 m (4 m - \sqrt{3}) - \sqrt{3} (4 m - \sqrt{3})$

Apply the distributive property.

$4 m (4 m) + 4 m (- \sqrt{3}) - \sqrt{3} (4 m - \sqrt{3})$

Apply the distributive property.

$4 m (4 m) + 4 m (- \sqrt{3}) - \sqrt{3} (4 m) - \sqrt{3} (- \sqrt{3})$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 m \cdot m + 4 m (- \sqrt{3}) - \sqrt{3} (4 m) - \sqrt{3} (- \sqrt{3})$

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

$4 \cdot 4 (m \cdot m) + 4 m (- \sqrt{3}) - \sqrt{3} (4 m) - \sqrt{3} (- \sqrt{3})$

Multiply $m$ by $m$ .

$4 \cdot 4 m^{2} + 4 m (- \sqrt{3}) - \sqrt{3} (4 m) - \sqrt{3} (- \sqrt{3})$

Multiply $4$ by $4$ .

$16 m^{2} + 4 m (- \sqrt{3}) - \sqrt{3} (4 m) - \sqrt{3} (- \sqrt{3})$

Multiply $- 1$ by $4$ .

$16 m^{2} - 4 m \sqrt{3} - \sqrt{3} (4 m) - \sqrt{3} (- \sqrt{3})$

Multiply $4$ by $- 1$ .

$16 m^{2} - 4 m \sqrt{3} - 4 \sqrt{3} m - \sqrt{3} (- \sqrt{3})$

Multiply $- \sqrt{3} (- \sqrt{3})$ .

Multiply $- 1$ by $- 1$ .

$16 m^{2} - 4 m \sqrt{3} - 4 \sqrt{3} m + 1 \sqrt{3} \sqrt{3}$

Multiply $\sqrt{3}$ by $1$ .

$16 m^{2} - 4 m \sqrt{3} - 4 \sqrt{3} m + \sqrt{3} \sqrt{3}$

Raise $\sqrt{3}$ to the power of $1$ .

$16 m^{2} - 4 m \sqrt{3} - 4 \sqrt{3} m + {\sqrt{3}}^{1} \sqrt{3}$

Raise $\sqrt{3}$ to the power of $1$ .

$16 m^{2} - 4 m \sqrt{3} - 4 \sqrt{3} m + {\sqrt{3}}^{1} {\sqrt{3}}^{1}$

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

$16 m^{2} - 4 m \sqrt{3} - 4 \sqrt{3} m + {\sqrt{3}}^{1 + 1}$

Add $1$ and $1$ .

$16 m^{2} - 4 m \sqrt{3} - 4 \sqrt{3} m + {\sqrt{3}}^{2}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$16 m^{2} - 4 m \sqrt{3} - 4 \sqrt{3} m + {(3^{\frac{1}{2}})}^{2}$

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

$16 m^{2} - 4 m \sqrt{3} - 4 \sqrt{3} m + 3^{\frac{1}{2} \cdot 2}$

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

$16 m^{2} - 4 m \sqrt{3} - 4 \sqrt{3} m + 3^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 m^{2} - 4 m \sqrt{3} - 4 \sqrt{3} m + 3^{\frac{2}{2}}$

Rewrite the expression.

$16 m^{2} - 4 m \sqrt{3} - 4 \sqrt{3} m + 3^{1}$

Evaluate the exponent.

$16 m^{2} - 4 m \sqrt{3} - 4 \sqrt{3} m + 3$

Reorder the factors of $- 4 \sqrt{3} m$ .

$16 m^{2} - 4 m \sqrt{3} - 4 m \sqrt{3} + 3$

Subtract $4 m \sqrt{3}$ from $- 4 m \sqrt{3}$ .

$16 m^{2} - 8 m \sqrt{3} + 3$

Simplify (4m- square root of 3)(4m- square root of 3)

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