Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

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

Step 2.1.2

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

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Step 2.1.2.1

Move $m$ .

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

Step 2.1.2.2

Multiply $m$ by $m$ .

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

Step 2.1.3

Multiply $4$ by $4$ .

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

Step 2.1.4

Multiply $- 1$ by $4$ .

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

Step 2.1.5

Multiply $4$ by $- 1$ .

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

Step 2.1.6

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

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Step 2.1.6.1

Multiply $- 1$ by $- 1$ .

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

Step 2.1.6.2

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

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

Step 2.1.6.3

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

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

Step 2.1.6.4

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

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

Step 2.1.6.5

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

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

Step 2.1.6.6

Add $1$ and $1$ .

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

Step 2.1.7

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

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Step 2.1.7.1

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

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

Step 2.1.7.2

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

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

Step 2.1.7.3

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

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

Step 2.1.7.4

Cancel the common factor of $2$ .

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Step 2.1.7.4.1

Cancel the common factor.

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

Step 2.1.7.4.2

Rewrite the expression.

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

Step 2.1.7.5

Evaluate the exponent.

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

Step 2.2

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

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

Step 2.3

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

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